SSLC Question Bank - Mathematics

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1. ¥À±ÀßPÉÆÃpAiÀÄ GzÉÝ±ÀåUÀ¼ÀÄ:

• ¸ÁPÀµÀÄÖ ªÉÊ«zsÀå¥ÀÇtð, G¢ÝµÀÖUÀ¼À£ÀÄß ºÉÆA¢PÉÆAqÀAvÉ «µÀAiÀÄUÀ¼À ªÉÄÃ¯É ¥Àæ±ÉßUÀ¼À£ÀÄß ¸ÀAUÀæ»¸ÀÄ«PÉ.

• «±Áé¸À¤ÃAiÀÄ, ºÁUÀÆ CxÀð¥ÀÇtðªÁzÀ ¥ÀjÃPÀëtUÀ¼À£ÀÄß ¸ÁªÀÄxÁåðzsÁjvÀ eÉÆÃr¸ÀÄ«PÉ.

• ««zsÀ ªÀÄlÖzÀ PÁp£ÀåvÉUÀ£ÀÄUÀÄtªÁV ¥Àæ±ÉßUÀ¼À eÉÆÃqÀuÉ.

• ¤gÀAvÀgÀ ¥ÀjÃ²Ã®£ÉUÉ M¼À¥Àr¸ÀÄªÀ CªÀPÁ±À ºÉÆA¢gÀ¨ÉÃPÁVzÉ.

2. ¥Àæ±ÀßPÉÆÃpAiÀÄ gÀÆ¥ÀgÉÃSÉ: • «µÀAiÀÄ «±ÉèÃµÀuÉ - «µÀAiÀÄUÀ¼À ºÀAaPÉ

• ¥ÀæwWÀlPÀzÀ°è G¢Ý±ÀåªÁgÀÄ ºÀAaPÉ - ¸ÁªÀÄxÁåðªÁgÀÄ ºÀAaPÉ

• ¥Àæ±ÉßAiÀÄ «zsÁ£À ºÀAaPÉ

- §ºÀÄ DAiÉÄÌ (1 CAPÀ) - QgÀÄ GvÀÛgÀ (2 CAPÀUÀ¼ÀÄ) - ¢ÃWÀð GvÀÛgÀ (3-4 CAPÀUÀ¼ÀÄ)

• PÀptvÉAiÀÄ ªÀÄlÖ - (¸ÀÄ®¨sÀ, PÀµÀÖ, ¸ÁzsÁgÀt)

• §ºÀÄDAiÉÄÌ GvÀÛgÀ ¥ÀnÖ, ºÁUÀÆ ¸ÀtÚ GvÀÛgÀ ªÀÄvÀÄÛ ¢ÃWÀð GvÀÛgÀUÀ¼À CAPÀ «vÀgÀuÉ.

3. ¥Àæ±ÀßPÉÆÃpAiÀÄ G¥ÀAiÉÆÃUÀUÀ¼ÀÄ: • ªÉÊW¯ÓW¯ÓW¯ÓW¯Ó¤PÀªÁV ¥Àæ±Àß¥ÀwæPÉUÀ¼À£ÀÄß vÀAiÀiÁj¸ÀÄªÀ°è ²PÀëPÀjUÉ £ÉgÀªÀÅ.

• ¨ÉÆÃzsÀ£Á UÀÄtªÀÄlÖ ºÉaÑ¸ÀÄªÀÅzÀÄ.

• ««zsÀ GzÉÝÃ±ÀUÀ½UÀ£ÀÄUÀÄtªÁV ¥Àæ±ÀßPÉÆÃp vÀAiÀiÁjPÉ (GzÁ: ¸ÁzsÀ£É, DAiÉÄÌ, ¥ÉÇæªÉÆÃµÀ£À¯ï ºÁUÀÆ £ÀÆå£ÀvÁ ¥Àj±ÉÆzsÀ£À, EvÁå¢).

• «µÀAiÀÄ «±ÉèÃµÀuÉAiÀÄ£ÀÄß PÀÆ®APÀÄ±ÀªÁV CxÀð¥ÀÇtðªÁV ªÀiÁqÀÄªÀÅzÀgÀ°è ²PÀëPÀjUÀÆ ºÁUÀÆ «zÁåyðUÀ½UÀÆ ¸ÀºÁAiÀÄPÀ.

• ²PÀëPÀgÀÄ vÀªÀÄä YõÁÕ£ÀªÀ£ÀÄß ¨ÉÆÃzsÀ£ÁPË±À®åªÀ£ÀÄß ºÉaÑ¹PÉÆ¼Àî®Ä ¸ÀºÀPÁj.

• EµÉÆÖAzÀÄ C£ÀÄPÀÆ®vÉUÀ½gÀÄªÀ ¥Àæ±ÀßPÉÆÃpUÀ¼À£ÀÄß ¸ÀAWÀn¸ÀÄªÀ°è M¼ÉîAiÀÄ £ÀªÀÄÆ£É ¥Àæ±ÉßUÀ¼À£ÀÄß eÉÆÃr¸ÀÄvÁÛºÉÆÃUÀÄªÀÅzÀÄ ªÁrPÉ.

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• F £ÀªÀÄÆ£É ¥Àæ±ÉßUÀ¼À°è ªÀÄÆ® ªÁPÁåA±À(stem) / ¥Àæ±Éß JA§ ªÉÆzÀ® ¨sÁUÀ ºÁUÀÆ F ¥Àæ±ÉßUÉ ¸ÀÆavÀ 4 DAiÉÄÌUÀ¼ÀÄ EgÀÄªÀªÀÅ. • ¥Àæ±ÉßAiÀÄ ªÀÄÆ®ªÁPÁåA±À ¥Àæ±ÉßAiÀÄ gÀÆ¥ÀzÀ°ègÀÄªÀÅzÉÃ ¸Àj. PÉ®ªÉÇªÉÄä ÇÀA¥ÀÇtð ªÁPÀå«gÀ§ºÀÄzÀÄ, ºÁVzÁÝUÀ ÇÀA¥ÀÇtð¥ÀzÀ ªÁPÀåzÀ

PÉÆ£ÉAiÀÄ¯ÉèÃ EgÀ¨ÉÃPÀÄ. • 4 DAiÉÄÌUÀ¼ÀÆ ¸À«ÄÃ¥À / GvÀÛgÀUÀ¼ÁVzÀÄÝ MAzÀÄ ªÀiÁvÀæ ¸ÀªÀÄAd¸À GvÀÛgÀªÁVgÀÄªÀAvÉ gÀa¸À¨ÉÃPÀÄ. 4 DAiÉÄÌUÀ¼ÀÄ «©ü£Àß «ZÁgÀUÀ½UÉ

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F PÁAiÀÄðPÉÌ ¸ÀjAiÀiÁzÀ MvÀÄÛ PÉÆlÄÖ, ªÀÄÄAzÀÆr ±Àæ«Ä¸ÀÄwÛgÀÄªÀ r.J¸ï.E.Dgï.n ¤zÉðÃ±ÀPÀgÁzÀ r.dUÀ£ÁßxÀgÁªï ºÁUÀÆ PÀ£ÁðlPÀ ¥ÀjÃPÁë ªÀÄAqÀ½ ¤zÉðÃ±ÀPÀgÁzÀ ²æÃ.n.JªÀiï. PÀÄªÀiÁgï gÀªÀjUÀÆ £ÀªÀÄä ºÀÈvÀÆàªÀðPÀ C©ü£ÀAzÀ£ÉUÀ¼ÀÄ ºÁUÀÆ ªÀAzÀ£ÉUÀ¼ÀÄ. EzÉÃ jÃw r.J¸ï.E.Dgï.n AiÀÄ PÀbÉÃjAiÀÄ°è£À D¦üÃ¸Àgï DzÀ ²æÃªÀÄw. ¹jAiÀÄtÚªÀgï ®°vÁ ZÀAzÀæ±ÉÃRgï gÀªÀgÀÄ ºÁUÀÆ J®è gÀZÀ£Á ¸À«Äw ¸ÀzÀ¸ÀågÀÄUÀ½UÀÆ £ÁªÀÅ F ªÀÄÆ®PÀ ªÀAzÀ£ÉUÀ¼À£ÀÄß ¸À°è¸ÀÄvÉÛÃªÉ.

qÁ:n.PÉ.dAiÀÄ®Që÷

qÁ: r. J¸ï.²ªÁ£ÀAzÀ ************

List of Abbreviations Used Part I Multiple Choice Questions

Part II Short and Long Answer type Questions

Abbreviations Meaning Item Number

Code

Meaning

Languages KF Kannada First Language L.No Lesson Number KS Kannada Second/Third Language PR Prose EF English First Language PO Poem ES English Second Language Gr Grammar HF Hindi First Language

Comp Comprehension HT Hindi Third Language Core Subjects SF Sanskrit First Language

Ch.No Chapter Number ST Sanskrit Third Language B Biology U Urdu Social Studies Ma Marathi H History Ta Tamil C Civics Te Telugu G Geography M Mathematics E Economics SC Science SS Social Studies

Obj Objectives UÀ UÀzÀå

K Knowledge ¥À ¥ÀzÀå

Languages G G¢ÝµÀÖ

C Comprehension YõÁÕ YõÁÕ£À÷

A Appreciation ¨sÁ ¨sÁµÉ

E Expression UÀæ UÀæ»PÉ

Core Subjects ¥Àæ ¥Àæ±ÀA¸É

U Understanding C C©üªÀåQÛ

A Application PÀ.ªÀÄlÖ PÀp£ÀvÉAiÀÄ ªÀÄlÖ

S Skill ¸ÀÄ ¸ÀÄ®¨sÀ

Diff.level Difficulty level ¸Á ¸ÁzsÁgÀt

E Easy PÀ PÀµÀÖ

A Average G G¢ÝµÀÖ

D Difficult

D.S.E.R.T

#4, 100 fT ring road, Banashankari III stage, Bangalore – 85

Sample Items of X Standard Question Bank Subject: Mathematics

sÁUÀ I Part I Item

No. Questions Ch.No Obj Key Diff.

Level

M001 ¸ÀAPÉÃvÀUÀ¼À°è ¸ÀÆa¹gÀÄªÀ F PÉ¼ÀV£À ¤AiÀÄªÀÄªÀ£ÀÄß ºÉ Àj¹ - (P∪Q)∪R = R∪(P∪Q)

A. ¸ÀºÀªÀvÀð£À ¤AiÀÄªÀÄ B. « sÁdPÀ ¤AiÀÄªÀÄ C. ¥ÀjªÀvÀð£À ¤AiÀÄªÀÄ D. rªÀiÁUÉÆðÃ£À£À ¤AiÀÄªÀÄ Name the law that is symbolically stated as (P∪Q)∪R = R∪(P∪Q) A. Associative Law B. Distributive Law C. Commutative Law D. De Morgan’s Law

1 K C E

M002 UÀt A = {1,2,3,4,5}, B={0,1,2,3,4} ªÀÄvÀÄÛ UÀt C= {-2, -1, 0, +1, +2} DzÀgÉ, ±ÀÆ£ÀåUÀtªÀÅ PÉ¼ÀV£À AiÀiÁªÀ UàtUÀ¼À G¥ÀUÀtªÁVzÉ? A. B ªÀÄvÀÄÛ C B. A ªÀÄvÀÄÛ C C. A ªÀÄvÀÄÛ B D. A, B ªÀÄvÀÄÛ C If set A = {1,2,3,4,5}, B={0,1,2,3,4} and C= {-2, -1, 0, +1, +2},empty set is a subset of which of the following sets? A. B and C B. A and C C. A and B D. A, B and C

1 K D E

M003 PÉ¼ÀV£À ªÉÉ£ï£ÀÀPÉëUÀ¼À°è AiÀiÁªÀÅzÀÄ (B-A) £ÀÄß ¥Àæw¤¢ü ÀÄvÀÛzÉ?

Which of the following Venn diagrams represents B-A?

1

U

D

E

Item


Level

M004 PÉÆnÖgÀÄªÀ ªÉ£ï£ÀPÉëUÀ¼À°è PÀ£ÀßqÀ ªÀÄvÀÄÛ EAVèµï ¢£À ¥ÀwæPÉUÀ¼À£ÀÄß NzÀÄªÀªÀgÀ ¸ÀASÉåAiÀÄ£ÀÄß vÉÆÃj¸ÀÄvÀÛzÉ. EªÀÅUÀ¼À°è AiÀiÁªÀ avÀæªÀÅ JgÀqÀÄ ¨sÁµÉUÀ¼À°è NzÀÄªÀªÀgÀ ¸ÀASÉåAiÀÄ£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä ¸ÀºÁAiÀÄPÀªÁVzÉ?

Given venn diagrams shows the number of people who read Kannada and English newspapers. Which diagram helps in finding the number who read both the news papers? Given Venn diagrams shows the number of people who read Kannada and English newspapers. Which diagram helps in finding the number who read both the news papers?

1

A

C E

M005 U={0, 1, 2, 3, 4, 5,6}, A= {0,2,4} B= {0,2,3,5} DzÀgÉ (A∪ B) UÀtªÀÅ :

A. {1, 6} B. {0, 2, 4} C. Ø D. {0,2,3,5}

If U={0, 1, 2, 3, 4, 5,6}, A= {0,2,4} B= {0,2,3,5} (A∪ B) is :

A. {1, 6} B. {0, 2, 4} C. Ø D. {0,2,3,5}

1 U A A

M006 PÉ¼ÀV£À ¸ÀASÁåUÀtUÀ¼À°è AiÀiÁªÀÅzÀÄ ±ÉæÃrüAiÀiÁVzÉ?

A. 4, 5, 7, 1, 13 B. 4, 3, 4, 3, 4 C. 10, 8, 3, 2, 1 D. 1, 4, 3, 5, 2 Which of the following set of numbers form a sequence? A. 4, 5, 7, 1, 13 B. 4, 3, 4, 3, 4 C. 10, 8, 3, 2, 1 D. 1, 4, 3, 5, 2

1 K B E

E K

Item


Level

M007 4+7+10+13+-----+ n ±ÉæÃrüAiÀÄ MA§vÀÛ£ÉAiÀÄ ¥ÀzÀ

A. 19 B. 28 C. 40 D. 50

The ninth term of the series : 4+7+10+13+-----+ n

A. 19 B. 28 C. 40 D. 50

1 K B A

M008 P¼ÀV£À AiÀiÁªÀ ¸ÀÆvÀæ¢AzÀ, ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ n£ÉÃ ¥ÀzÀªÀ£ÀÄß PÀAqÀÄ»rAiÀÄ§ºÀÄzÀÄ?

A. Tn = a + n-d B. Tn = a + (n-1)d C. Tn = a (n-1)d D. Tn = a + n-1 d

Which of the following is the formula to find the nth term of an arithmetic progression?

A. Tn = a + n-d B. Tn = a + (n-1)d C. Tn = a (n-1)d D. Tn = a + n-1 d

1 K B E

M009 MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ ªÉÆzÀ®£É ¥ÀzÀ 3 ªÀÄvÀÄÛ ¸ÁªÀiÁ£Àå ªÀåvÁå¸À 5 DzÁUÀ, n£ÉÃ ¥ÀzÀªÀÅ,

A. n- 2 B. 5n -2 C. 5n +8 D. 3n

The first term of an A.P is 3 and common difference is 5 then the nth term is

A. n- 2 B. 5n -2 C. 5n +8 D. 3n

1 S B E

M010 PÉ¼ÀV£À AiÀiÁªÀÅzÀÄ ¤dªÁzÀ UÀtÂvÀ ¸ÀA sÀAzÀªÁVzÉ?

A. Sn + Tn = S n-1 B. Sn – S n+1 = Tn C. Sn – S n-1 =Tn D. Sn + Tn = S n+1 Which of the following is a true mathematical relation?

A. Sn + Tn = S n-1 B. Sn – S n+1 = Tn C. Sn – S n-1 =Tn D. Sn + Tn = S n+1

1 K C A

M011 MAzÀÄ ªÀiÁvÀÈPÉAiÀÄÄ CzÀgÀ ¸ÀÜ¼ÁAvÀj¹zÀ ªÀiÁvÀÈPÉUÉ ¸ÀªÀÄ£ÁzÀgÉ CzÀÄ F ªÀiÁvÀÈPÉAiÀiÁUÀÄvÀÛzÉ.

A. CqÀØ¸Á®Ä B. PÀA§¸Á®Ä C. ÇÀªÀÄ«Äw D. ÀªÀÄ«Äw

If a matrix is equal to its transpose then the matrix is:

A. Row B. Column C. Skew symmetric D. symmetric 1 K D E

Item


Level

M012 x ªÀÄvÀÄÛ y UÀ¼À AiÀiÁªÀ É ÉUÀ¼ÀÄ ªÀiÁvÀÈPÉ 1 x 3 AiÀÄ£ÀÄß ¸ÀªÀÄ«Äw ªÀiÁvÀÈPÉ ªÀiÁqÀÄªÀÅzÀÄ?

2 3 4

3 y 5

A. 3, 3 B. 1, 5 C. 2, 4 D. 4, 2

What values of x and y makes the matrix 1 x 3 a symmetric matrix?

2 3 4

3 y 5

A. 3, 3 B. 1, 5 C. 2, 4 D. 4, 2 1 U C E

M013 MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ°è T10=20 ; T20=10 DzÀgÉ ¸ÁªÀiÁ£Àå ªÉåvÁå¸À JµÀÄÖ?

A. 2 B. 15 C. +1 D. –1

If T10=20 and T20=10 in an A.P, what is the common difference?

A. 2 B. 15 C. +1 D. -1

1 U D A

M014 £À£Àß ªÀÄUÀ£À ªÀAiÀÄ¸ÀÄì, £À£Àß vÀAzÉAiÀÄ ªÀAiÀÄ¸ÀÄì ªÀÄvÀÄÛ £À£Àß ªÀAiÀÄ¸ÀÄì EªÀÅUÀ¼É Áè ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ°èªÉ. £À£Àß ªÀAiÀÄ¸ÀÄì 40, ºÁUÀÆ £À£Àß ªÀÄUÀ£À ªÀAiÀÄ¸ÀÄì 10 ªÀµÀðUÀ¼ÁzÀgÉ, £À£Àß vÀAzÉAiÀÄ ªÀAiÀÄ¸ÉìµÀÄÖ?

A. 50 B. 60 C. 70 D. 80

My son’s age, father’s age and my age are in AP. If my age is 40 and my son’s is 10, what is the age of my father?

A. 50 B. 60 C. 70 D. 80

1 A C A

Item


Level

M015 A+I = 2 1 DzÁUÀ, ªÀiÁvÀÈPÉ A UÉ ¸ÀªÀÄ£ÁzÀÄzÀÄ,

1 0

1 0 1 1 1 0 1 1

A. 0 1 B. 1 -1 C. 0 -1 D. 0 -1

If A+ I = 2 1 then, matrix A is equal to

1 0

1 0 1 1 1 0 1 1

A. 0 1 B. 1 -1 C. 0 -1 D. 0 -1 1 S B A

M016 PÀæªÀÄ AiÉÆÃd£ÉAiÀÄ CxÀðªÀ£ÀÄß PÉÆqÀÄªÀ ºÉÃ½PÉ

A. vÉÆÃl¢AzÀ gÉÆÃeÁ ºÀÆUÀ¼À£ÀÄß Dj¸ÀÄªÀÅzÀÄ B. §ÄnÖAiÀÄ°ègÀÄªÀ ºÀÆªÀÅUÀ¼À£ÀÄß Dj¸ÀÄªÀÅzÀÄ

C. PÁªÀÄ£À©°è£À°ègÀÄªÀ §tÚUÀ¼À eÉÆÃqÀuÉ D. UÀæAxÁ®AiÀÄzÀ°è£À ¥ÀÄ¸ÀÛPÀUÀ¼À DAiÉÄÌ

The statement which gives the meaning of permutation is : A. Picking flowers in the rose garden B. Choosing different flowers in a basket

C. Arrangement of colours in a rainbow D. Selecting the books in a library

2

K

C

E

M017 5 ««zsÀ ¥ÀÄ¸ÀÛPÀUÀ¼À£ÀÄß ÉÃgÉ ÉÃgÉ jÃwAiÀÄ°è eÉÆÃr¸ÀÄªÀÅzÀ£ÀÄß »ÃUÉ ¸ÀÆa¸À§ºÀÄzÀÄ?

A. 5P2 B. 5P3 C.

5P4 D. 5P5

Arrangement of 5 different books in different ways can be denoted as: A. 5P2 B.

5P3 C. 5P4 D. 5P5 2 K D E

Item

No.

Questions Ch.No Obj Key

Diff.

Level

M018 nC8 = nC12 DzÁUÀ n = 20 EzÀ£ÀÄß ¯ÉQÌ¸À®Ä G¥ÀAiÉÆÃV¸ÀÄªÀ ¸À«ÄÃPÀgÀt:

A. nC1 = n B. nC r = nPr /r! C. nCr =

nC n-r D. nCn = 1 If nC8 = nC12 then n = 20. this can be calculated using the relation:

A. nC1 = n B. nC r = nPr /r! C. nCr =

nC n-r D. nCn = 1

2 K C A

M019 nC15 = nC11 £À°è ‘n’ £À É¯ÉAiÀÄ£ÀÄß PÀAqÀÄ»rAiÀÄÄªÀ ªÉÆzÀ® ºÀAvÀ nCr £ÀÄß nCn-r UÉ ¥ÀjªÀwð¸ÀÄªÀÅzÀÄ JgÀqÀ£ÉÃ ºÀAvÀ:

A. n+15=n+11 B. 15=n+11 C. 15=n-11 D. 11= n-15

nC15 = nC11 to find the value of ‘n’ the first step is converting nCr into nCn-r. Second step is: A. n+15=n+11 B. 15=n+11 C. 15=n-11 D. 11= n-15 2 K C E

M020 DgÀÄ d£ÀgÀ°è C±ÉÆÃPÀ£ÀÆ M§â. F UÀÄA¦¤AzÀ C±ÉÆÃPÀ£À£ÀÄß ¸ÉÃj¹zÀAvÉ 4 d£ÀgÀ£ÀÄß JµÀÄÖ «zsÀUÀ¼À°è Dj¸À§ºÀÄzÀÄ?

A. 10 B. 15 C. 20 D. 60

Ashok is one among 6 people. In how many ways can 4 people be selected from them, so as to include Ashok?

A. 10 B. 15 C. 20 D. 60 2 K A A

M021 PÉÆnÖgÀÄªÀ AiÀiÁªÀ ºÉÃ½PÉUÀ¼ÀÄ nCr = nCn-r ¤§AzsÀ£ÉAiÀÄ£ÀÄß C£ÀÄ¸Àj¸ÀÄªÀÅzÀÄ?

A. 10C8 = 10C4 B. 10C8 = 10C2 C. 10C8 = 10C3 D. 10C5 = 10C2

Which of the following satisfy the relation nCr = nCn-r?

A. 10C8 = 10C4 B. 10C8 = 10C2 C. 10C8 = 10C3 D. 10C5 =10C2 2 K B E

M022 7 §tÚUÀ½AzÀ ¥ÀæwzsÀédzÀ®Æè ¥ÀÄ£ÀgÁªÀwð¸ÀzÉ ««zsÀ ¤¢üðµÀÖ §tÚUÀ¼À£ÀÄß ¸ÀjºÉÆAzÀÄªÀAvÉ 210 zsÀédUÀ¼À£ÀÄß ªÀiÁqÀ§ºÀÄzÁzÀgÉ ¥Àæw zsÀédzÀ°è£À §tÚUÀ¼À ¸ÀASÉå:

A. 2 B. 3 C. 4 D. 5

Among 7 colours 210 different flags are formed with a certain equal number of colours without repetition. Number of colours in each flag is: A. 2 B. 3 C. 4 D. 5 2 A B A

Item

No.

Questions

Ch.No Obj Key

Diff.

Level

M023 nP2 = 2 × n-1 P3 , DzÀÝjAzÀ n(n-1) = 2 × -----------. E°è vÀÀ¦àºÉÆÃVgÀÄªÀ ¥ÀzÀªÀÅ :

A. n(n+1) (n+2) B. n(n-1) (n-2) C. (n-1) (n-2) (n-3) D. (n-1) (n) (n+1)

nP2 = 2 × n-1 P3 , therefore n(n-1) = 2 × -----------. Here the missing term is:

A. n(n+1) (n+2) B. n(n-1) (n-2) C. (n-1) (n-2) (n-3) D. (n-1) (n) (n+1) 2 A C A

M024 5 ««zsÀ ¤WÀAlÄUÀ¼ÀÄ ªÀÄvÀÄÛ 4 ««zsÀ ªÁåPÀgÀt ¥ÀÄ¸ÀÛPÀUÀ¼À£ÀÄß MAzÉÃ jÃwAiÀÄ ¥ÀÄ¸ÀÛPÀUÀ¼ÀÄ MnÖUÉ EgÀÄªÀAvÉ PÀ¥Án£À°è eÉÆÃr¹zÁUÀ ¸ÁzsÀåªÁUÀÄªÀ eÉÆÃqÀuÉUÀ¼À «zsÀUÀ¼À ¸ÀASÉå:

A. 5! + 4! B. 5! × 4! C. 5! + 4! + 2! D. 5! × 4! × 2!

5 different dictionaries and 4 different grammar books are arranged in a shelf such that same books are together. Number of arrangements are: A. 5! + 4! B. 5! × 4! C. 5! + 4! + 2! D. 5! × 4! × 2! 2 U D D

M025 5C2 É ÉAiÀÄ£ÀÄß PÀAqÀÄ »rAiÀÄÄªÁUÀ C£ÀÄ¸Àj¹gÀÄªÀ vÀ¥ÀÄà ºÀAvÀªÀ£ÀÄß UÀÄgÀÄw¹:

ºÀAvÀ 1 = 5! . ºÀAvÀ 2 = 5! ºÀAvÀ 3 = 5x4x3x2x1 ºÀAvÀ 4 = 10

5-2! 3! 3x2x1 A. ºÀAvÀ 1 B. ºÀAvÀ 2 C. ºÀAvÀ 3 D. ºÀAvÀ 4

Identify the wrong step while finding the value of 5C2 :

Step 1 = 5! . Step 2 = 5! Step 3 = 5x4x3x2x1 Step 4 = 10

5-2! 3! 3x2x1 A. Step 1 B. Step 2 C. Step 3 D. Step 4 2 A A A

M026 MAzÀÄ QæPÉmï ¸ÀAWÀzÀ°è 10 vÀAqÀUÀ¼ÀÄ sÁUÀªÀ»¸ÀÄwÛªÉ. ¥Àæw vÀAqÀªÀÅ JgÀqÉgÀqÀÄ ¨Áj EvÀgÉ vÀAqÀzÉÆqÀ£É DqÀ ÉÃPÁzÀgÉ, DrzÀ DlUÀ¼À ¸ÀASÉå

A. 2×10P2 B. 2×10C2 C. 2+10P2 D. 2+10C2

In a cricket league there are 10 teams competing. Each team has to play with every other team twice. The number of games to be played is : A. 2×10P2 B. 2×10C2 C. 2+

10P2 D. 2+10C2 2 U B A

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M027 ‘n’ ¨ÁºÀÄUÀ½gÀÄªÀ §ºÀÄ sÀÄdzÀ°è£À PÀtðUÀ¼À ¸ÀASÉå [nc2 – n] PÀtðUÀ¼À£ÀÄß M¼ÀUÉÆAqÀAvÉ 10 gÉÃSÁRAqÀUÀ½zÀÝgÉ D §ºÀÄ sÀÄeÁPÀÈwAiÀÄÄ:

A. ¥ÀAZÀ sÀÄd B. µÀqÀÄâd C. CµÀÖ sÀÄd D. zÀ±À sÀÄd

A polygon of ‘n’ sides has [nc2 – n] diagonals. If number of line segments including diagonals are 10, the polygon is: A. Pentagon B. Hexagon C. Octagon D. Decagon 2 U A A

M028 5 ¸ÀªÀiÁAvÀgÀ gÉÃSÉUÀ¼À UÀÄA¥À£ÀÄß 3 ¸ÀªÀiÁAvÀgÀ gÉÃSÉUÀ¼ÀÄ PÀvÀÛj¹zÁUÀ GAmÁUÀÄªÀ ¸ÀªÀiÁAvÀgÀ ZÀvÀÄ sÀÄðdUÀ¼À ¸ÀASÉå

A. 120 B. 60 C. 30 D. 15

Number of parallelograms that can be formed by a set of 5 parallel lines intersecting with 3 other parallel lines are: A. 120 B. 60 C. 30 D. 15 2 S C A

M029 «µÀÄÚ«£À «UÀæºÀzÀ £Á®ÄÌ PÉÊUÀ¼À°è, zÀAqÀ, ZÀPÀæ, ±ÀAR ªÀÄvÀÄÛ ¥ÀzÀäUÀ½ªÉ. EAvÀºÀ 12 «UÀæºÀUÀ¼À£ÀÄß ªÀiÁqÀ ÉÃPÁzÀgÉ PÉÊUÀ¼À°è£À aºÉßUÀ¼À£ÀÄß ¤ªÀð»¸À§ºÀÄzÁzÀ «zsÀUÀ¼À£ÀÄß »ÃUÉ ¥Àæw¤¢ü À§ºÀÄzÀÄ:

A. 4P1 B. 4P2 C. 4P3 D. 4P4

An idol of Vishnu has a mace, chakra, shanka and padma in each of the four hands. To make 12 such idols, the number of ways in which the symbols in the hands have to be manipulated is represented as: A. 4P1 B. 4P2 C. 4P3 D. 4P4 2 A B A

M030 σ = ¥Àæ¸ÀgÀuÉAiÀÄ «ZÀ®£É, F ªÁPÀåªÀÅ ¸ÀÆa¸ÀÄªÀÅzÀÄ:

A. ªÀiÁ£ÀPÀ«ZÀ®£É B. ªÀiÁ¦ð£À UÀÄuÁAPÀ C. ÀgÁ¸Àj D. ¸ÀgÁ¸Àj «ZÀ®£É

The expression σ = variance, represents: A. Standard deviation B. Coefficient of variation C. Mean D. Mean deviation 3 K A E

M031 ªÀUÁðAvÀgÀ 30-34 gÀ ªÀÄzsÀå©AzÀÄ:

A. 30 +34 B. ½ ( 30 + 34) C. ½ ( 34 -30) D. 34 -30

Mid point of the class interval 30 – 34 is:

A. 30 +34 B. ½ ( 30 + 34) C. ½ ( 34 -30) D. 34 -30 3 K B E

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M032 PÉÆnÖgÀÄªÀ zÀvÁÛA±ÀUÀ¼À£ÀÄß G¥ÀAiÉÆÃV¹PÉÆAqÀÄ ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄ£ÀÄß ¯ÉQÌ¸ÀÄ: N= 10, Σfx = 100 , Σfd2 = 210

A. 4.6 B. 5 C. 2.1 D. 21

Using the given data, calculate standard deviation N= 10, Σfx = 100 , Σfd2 = 210

A. 4.6 B. 5 C. 2.1 D. 21 3 S A E

M033 F PÉ¼ÀV£À ºÉÃ½PÉUÀ¼À°è AiÀiÁªÀÅzÀÄ ªÀiÁ¦ð£À UÀÄuÁAPÀPÉÌ ¸ÀA sÀAzÀ¥ÀnÖ®è?

A. ¸ÁªÀiÁ£ÀåªÁV ±ÉÃPÀqÁ jÃwAiÀÄ°è ºÉÃ¼À®àqÀÄvÀÛzÉ. B. ºÀgÀ«£À EAwµÀÄÖ ¸Á¥ÉÃPÀë C¼ÀvÉAiÀÄ jÃwAiÀÄ°è

C. KPÀªÀiÁ£ÀUÀ½®èzÀ ¥ÀjªÀiÁtªÁV D. PÉÃA¢æÃAiÀÄ ¥ÀæªÀèwÛAiÀÄ C¼ÀvÉ

Which of these statements is not related to co-efficient of variation

A. generally expressed in percentage B. relative measure of dispersion

C. independent of units D. measure of central tendency 3 U D E

M034 MAzÀÄ ±Á¯ÉAiÀÄ 9£É vÀgÀUÀwAiÀÄ A ªÀÄvÀÄÛ B ÉPÀë£ï UÀ¼ÀÄ UÀtÂvÀzÀ°è UÀ½¹gÀÄªÀ ¸ÀgÁ¸Àj CAPÀUÀ¼ÀÄ PÀæªÀÄªÁV 34.5 ªÀÄvÀÄÛ 28.5

DVzÀÄÝ, ªÀiÁ£ÀPÀ «ZÀ®£ÀªÀÅ 6.21 ªÀÄvÀÄÛ 4.56EzÀÝ°è, AiÀiÁªÀ ¸ÉPÀë£ï ¤£À ¸ÁzsÀ£ÉAiÀÄ°è C¹ÜvÀvÉ ºÉZÀÄÑ, PÁgÀtÂÃPÀj¹:

A. ¸ÉPÀë£ï A B. ÉPÀë£ï B C. ÉPÀë£ï A ªÀÄvÀÄÛ B JgÀqÀÆ D. ¸ÉPÀë£ï A ªÀÄvÀÄÛ B JgÀqÀgÀ°è MAzÀÆ C®è

If the arithmatic mean in maths of a 9th std., A & B sections in a school are 34.5 and 28.5 respectively and the Standard deviation are 6.21 and 4.56 respectively, in which section is the achievement unstable? A. Section A B. Section B C. Both section A and B D. Neither section A nor section B 3 U A A

M035 ‘n’ ªÀiË®åUÀ¼À ¸ÀgÁ¸Àj¬ÄAzÁzÀ «ZÀ®£ÉUÀ¼À ªÉÆvÀÛªÀÅ, AiÀiÁªÁUÀ®Æ:

A. -1 B. 0 C. +1 D. 1QÌAvÀ C¢üPÀ

The sum of deviation of a set of ‘n’ values from the arithmetic mean is always : A. -1 B. 0 C. +1 D. more than 1 3 K B A

M036 A, B ªÀÄvÀÄÛ C vÀgÀUÀwUÀ¼À CAPÀUÀ¼À£ÀÄß PÉÆqÀ¯ÁVzÉ. D vÀgÀUÀwUÀ¼À «ZÀ® ªÉÊ«zÀåvÉAiÀÄ£ÀÄß w½AiÀÄ®Ä, G¥ÀAiÉÆÃV¸À§ºÀÄzÁzÀÄzÀÄ:

A. ªÀÄzsÀåPÀ «ZÀ®£É B. ªÀiÁ¦ð£ÀÀ UÀÄuÁAPÀ C. ZÀvÀÄxÀðPÀ «ZÀ®£É D. ZÀvÀÄxÀðPÀ «ZÀ®£ÉAiÀÄ UÀtPÀ

Marks of three classes A, B and C are given. To find the heterogeneity of classes, the measure used is: A. Mean deviation B. Coefficient of variation C. Quartile deviation D. Coefficient of quartile deviation 3 U B A

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M037 1,2,3,4,5 ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄÄ 1.4 DzÀgÉ, 11, 12, 13, 14, 15 UÀ¼À ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄÄ:

A. 1.4 B. 2.8 C. 14 D. 28

If the standard deviation of 1,2,3,4,5 is 1.4, then the value of standard deviation of 11, 12, 13, 14, 15 is: A. 1.4 B. 2.8 C. 14 D. 28 3 U A E

M038 MAzÀÄ DªÀvÀð¥ÀnÖ¬ÄAzÀ, M§â «zÁåyðAiÀÄÄ X, d ªÀÄvÀÄÛ d2 UÀ¼À£ÀÄß PÀAqÀÄ»rAiÀÄÄvÁÛ£É. ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄ£ÀÄß PÀAqÀÄ »rAiÀÄ®Ä £ÁªÀÅ ¯ÉQÌ¸À ÉÃPÁzÀ ºÀAvÀªÀÅ

A. Σfd2 B. Σfd2 C. √ Σfd2 D. fd2

N N

A student finds X, D and D2 of a given frequency distribution. The next step in finding the S.D is to calculate. A. Σfd2 B. Σfd2 C. √ Σfd2 D. fd2

N N 3 U D A

M039 MAzÀÄ UÀÄA¦£À d£ÀgÀ ªÀAiÀÄ¸Àì£ÀÄß DªÀvÀð¥ÀnÖAiÀÄ°è ¥ÀnÖ ªÀiÁqÀ ÁVzÉ. EzÀgÀ ªÀUÁðAvÀgÀªÀ£ÀÄß ºÉaÑ¹zÁUÀ, F PÉ¼ÀV£ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ ºÉZÁÑUÀÄvÀÛzÉ?

A. MlÄÖ ªÀUÁðAvÀgÀUÀ¼À ¸ÀASÉå B. d£ÀgÀ ªÀAiÀÄ¸ÀÄì

C. MlÄÖ DªÀvÀðAPÁ D. ªÀUÁðAvÀgÀUÀ¼À M¼ÀV£À DªÀÈwÛ

The age of a set of people is tabulated in the form of a frequency distribution. Which one of the following increases, when the size of the class interval is increased? A. total number of class intervals B. ages of people

C. total frequency D. frequency within the class interval 3 U D D

M040 PÉ¼ÀV£ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ ‘3P’ AiÀÄ£ÀÄß ¸ÁªÀiÁ£Àå C¥ÀªÀvÀð£ÀªÁV ºÉÆA¢gÀÄªÀÅ¢®è?

A. 3P3 B. 6P2 C. 9P1 D. 12P0

Which of the following cannot have ‘3P’ as a common factor? A. 3P3 B. 6P2 C. 9P1 D. 12P0 4 K D E

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M041 ax2-a3 ªÀÄvÀÄÛ bx-ab UÀ¼À ªÀÄºÀvÀÛªÀÄ ¸ÁªÀiÁ£Àå C¥ÀªÀvÀð£ÀªÀÅ:

A. (x+a) B. (x-a) C. (x2-a2) D. (x2+a2)

Highest common factor of ax2-a3 and bx-ab is: A. (x+a) B. (x-a) C. (x2-a2) D. (x2+a2) 4 K B E

M042 x3y4z6 ªÀÄvÀÄÛ x6y2z4 UÀ¼À ®.¸Á.C. ªÀÅ

A. x3y4z6 B. x3y2z4 C. x6y4z6 D. x6y4z4

The L.C.M. of x3y4z6 and x6y2z4 is : A. x3y4z6 B. x3y2z4 C. x6y4z6 D. x6y4z4 4 K C E

M043 ªÀÄ.¸Á.C ªÀ£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä, 2x4 – x2 + 3x3 + 1 ©ÃdUÀÄZÀÒªÀ£ÀÄß §gÉzÀÄPÉÆ¼ÀÄîªÀ ¸ÀjAiÀiÁzÀ PÀæªÀÄ:

A. 2x4+3x3–x2+1 B. 2x4-3x3–x2+1 C. 2x4+3x3–x2+0x+1 D. 2x4+3x3–x2+x+1

Correct arrangement of terms of the expression 2x4 – x2 + 3x3 + 1 to find HCF is:

A. 2x4+3x3–x2+1 B. 2x4-3x3–x2+1 C. 2x4+3x3–x2+0x+1 D. 2x4+3x3–x2+x+1 4 K C E

M044 5x -10 ªÀÄvÀÄÛ 5x2 -20 UÀ¼À ªÀÄ.¸Á.C.ªÀÅ :

A. x-2 B. 5(x-2) C. 5x D. 5

HCF of 5x -10 and 5x2 -20 is

A. x-2 B. 5(x-2) C. 5x D. 5 4 S B E

M045 PÉ¼ÀV£ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ, ab (a+b)+bc(b+c)+ca(c+a) UÉ ÀªÀÄ£ÁVgÀÄªÀÅ¢®è :

A ∑ab (a+b) B. ∑c2 (a+b) C. ∑a2 (b+c) D. ∑b2 (a+b)

Which of the following is not equal to ab (a+b)+bc(b+c)+ca(c+a)? A ∑ab (a+b) B. ∑c2 (a+b) C. ∑a2 (b+c) D. ∑b2 (a+b) 4 S D A

M046 ∑a=0 DzÁUÀ, ∑a3 ªÀÅ :

A 0 B. abc C. 3abc D. a3+b3+c3

If ∑a=0, then ∑a3 will be: A 0 B. abc C. 3abc D. a3+b3+c3 4 S C A

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M047 ab2 –ac2 –a2b +bc2 –cb2 +ca2 £ÀÄß Σ ¸ÀAPÉÃvÀªÀ£ÀÄß G¥ÀAiÉÆÃV¹ §gÉ¬Äj:

a) Σ ab(a-b) b) Σ ab(b-a) c) Σ a (a-b) d) Σ b(a-b)

Write ab2 –ac2 –a2b +bc2 –cb2 +ca2 using Σ notation:

a) Σ ab(a-b) b) Σ ab(b-a) c) Σ a (a-b) d) Σ b(a-b) 4 S B E

M048 PÉ¼ÀV£ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀ£ÀÄß a3+b3+c3+3ab(a+b) UÉ PÀÆrzÁUÀ, CzÀÄ ZÀQæÃAiÀÄ ¸ÀªÀÄ«ÄwAiÀiÁUÀÄvÀÛzÉ?

A bc(b+a)+ca(c+a) B. 3bc(b+c)+ca(c+a)

C. 3 [bc(b+c)+ca(c+a)] D. 3abc [(b+c) + (c+a)]

Which of the following has to be added to a3+b3+c3+3ab(a+b) to make it cyclically symmetric? A bc(b+a)+ca(c+a) B. 3bc(b+c)+ca(c+a)

C. 3 [bc(b+c)+ca(c+a)] D. 3abc [(b+c) + (c+a)] 4 U C A

M049 ªÀÄÆgÀÄ ¸ÀASÉåUÀ¼À ªÉÆvÀÛ ‘0’ DVzÉ ªÀÄvÀÄÛ D ªÀÄÆgÀÄ ¸ÀASÉåUÀ¼À WÀ£ÀUÀ¼À ªÉÆvÀÛªÀÅ 36 DzÀgÉ, D ¸ÀASÉåUÀ¼À UÀÄt®§ÞªÀÅ:

A. 6 B. 12 C. 20 D. 30

If the sum of three numbers is zero and sum of their cubes is 36, then the product of three numbers is:

A. 6 B. 12 C. 20 D. 30 4 U B E

M050 (a-b)2=0 DzÁUÀ, F PÉ¼ÀV£À AiÀiÁªÀ ¸ÀA§AzsÀªÀÅ¤dªÁUÀÄvÀÛzÉ?

A. 2(a2+b2) =(a+b) 2 B. 2(a2+b2) =(a-b) 2 C. 2(a2-b2) =(a+b) 2 D. (a2-b2) =(a-b) 2

When (a-b)2=0, which of the following relations become true?

A. 2(a2+b2) =(a+b) 2 B. 2(a2+b2) =(a-b) 2 C. 2(a2-b2) =(a+b) 2 D. (a2-b2) =(a-b) 2 4 U A A

M051 (x2 +4x+4) (x2 +6x+9) gÀ ªÀUÀðªÀÄÆ®UÀ¼À É ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj:

A. x2+5x+6 B. x2+6x+5 C. x2-5x+6 D. x2+5x-6

Find the square root of (x2 +4x+4) (x2 +6x+9) :

A. x2+5x+6 B. x2+6x+5 C. x2-5x+6 D. x2+5x-6 4 S A E

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M052 1) √2 2) √12 3) √18 4) √200 F PÀgÀtÂUÀ¼À°è ¸ÀªÀÄgÀÆ¥À PÀgÀtÂUÀ¼ÀÄ

A. 1,2,3 B. 2,3,4 C. 1,2,4 D. 1,3,4

Like surds among the following are 1 ) √2 2) √12 3) √18 4) √200

A. 1,2,3 B. 2,3,4 C. 1,2,4 D. 1,3,4 4 K D A

M053 x √y = √80DzÀgÉ, DUÀ ‘y’£À É ÉAiÀÄÄ:

A. 4 B. 5 C. 8 D. 10

If x √y = √80, then the value of ‘y’ will be:

A. 4 B. 5 C. 8 D. 10 4 S B E

M054 2x√ x £À CPÀgÀtÂÃPÁgÀPÀ C¥ÀªÀvÀð£ÀªÀÅ

A. 2x√ x B. 2x + √ x C. 2x - √ x D. √ x

Rationalizing factor of 2x√ x is

A. 2x√ x B. 2x + √ x C. 2x - √ x D. √ x 4 K D A

M056 JgÀqÀ£ÉÃ WÁvÀzÀ°ègÀÄªÀ MAzÀÄ CªÀåPÀÛ¥ÀzÀªÀ£ÉÆß¼ÀUÉÆAqÀ MAzÀÄ §ºÀÄ¥ÀzÀ ©ÃeÉÆÃQÛAiÀÄ£ÀÄß »ÃUÉAzÀÄ PÀgÉAiÀÄ§ºÀÄzÀÄ.

A. ¢é¥ÀzÀ ©ÃeÉÆÃQÛ B. ¸ÀgÀ¼À §ºÀÄ¥ÀzÀ ©ÃeÉÆÃQÛ C.ªÀUÀð §ºÀÄ¥ÀzÀ ©ÃeÉÆÃQÛ D. §ºÀÄ¥ÀzÀ ©ÃeÉÆÃQÛ

A polynomial of degree two, in one variable is called:

A. a binomial B. a linear polynomial C. a quadratic polynomial D. polynomial 5 K C E

M057 ªÀUÀð¸À«ÄÃPÀgÀtzÀ DzÀ±Àð gÀÆ¥ÀªÁzÀ ax2+bx+c=0 zÀ°è b=0 DzÀgÉ GAmÁUÀÄªÀ ¸À«ÄÃPÀgÀtªÀÅ

A. ±ÀÄzÀÞ ªÀUÀð¸À«ÄÃPÀgÀt B. «Ä±Àæ ªÀUÀð¸À«ÄÃPÀgÀt C. £ÉÃgÀ D. ¸ÀgÀ¼À

In the standard form of the quadratic equation ax2+bx+c=0, if b=0 then the resulting equation is:

A. Pure quadratic B. adfected quadratic C. linear D. simple 5 K A E

M058 ax2+bx+c=0, ªÀUÀð¸À«ÆPÀgÀtzÀ ±ÉÆÃzsÀPÀ

A. –b2-4ac B. b2-4ac C. b2+4ac D. –b2 ±√b2-4ac

The discriminant of the quadratic equation ax2+bx+c=0 is:

A. –b2-4ac B. b2-4ac C. b2+4ac D. –b2 ±√b2-4ac 5 K B A

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M059 4k (3 k -1) = 5 DzÀ±Àð gÀÆ¥ÀªÀÅ :

A. 12 k 2-4k-5=0 B. 12 k 2-k-5=0 C. 12 k 2-4 k =5 D. 12 k 2-k =5 Standard from of 4k (3k -1) = 5 is:

A. 12 k 2-4k-5=0 B. 12 k 2-k-5=0 C. 12 k 2-4 k =5 D. 12 k 2-k =5 5 K A A

M060 ¥ÀÆtðªÀUÀðªÀ®èzÀ MAzÀÄ ªÀUÀð¸À«ÄÃPÀÀgÀt b2-4ac>0 DzÀgÉ, CzÀgÀ ªÀÄÆ®UÀ¼ÀÄ

A. ªÁ¸ÀÛªÀ B. ¸ÀªÀÄ C. ¸ÀA«Ä±Àæ D. ¨sÁUÀ®§Þ ¸ÀASÉå

In a quadratic equation if b2-4ac>0 and not a perfect square, then the roots are :

A. Real B. Equal C. Imaginary D. Rational 5 K A E

M061 PÉ¼ÀV£À ¸À«ÄÃPÀgÀtUÀ¼À°è ªÀÄÆ®UÀ¼ÀÄ ¸ÀªÀÄ£ÁVgÀÄªÀ ªÀUÀð¸À«ÄÃPÀgÀtªÀÅ:

A. x2-2x-1=0 B. x2-2x+1=0 C. 2x2-2x+1=0 D. x2-2x-3=0

Quadratic equation having equal roots among the following equation is :

A. x2-2x-1=0 B. x2-2x+1=0 C. 2x2-2x+1=0 D. x2-2x-3=0 5 U B A

M062 §ºÀÄ¥ÀzÀ x2-92 £ÀPÉëAiÀÄ£ÀÄß J¼ÉzÁUÀ gÉÃSÉAiÀÄÄ x- CPÀëªÀ£ÀÄß £ÀPÉëAiÀÄ£ÀÄß ÀA¢ü ÀÄªÀ ©AzÀÄUÀ¼ÀÄ

A. (-3, 0) ªÀÄvÀÄÛ (3,0) B. (-2, 0) ªÀÄvÀÄÛ (2,0) C. (-2, -5) ªÀÄvÀÄÛ (2,-5) D. (1,-8) ªÀÄvÀÄÛ (-1,-8)

When the graph of the polynomial x2-9 is drawn, the graph intersects the x- axis at the points

A. (-3, 0) and (3,0) B. (-2, 0) and (2,0) C. (-2, -5) and (2,-5) D. (1,-8) and (-1,-8) 5 U A A

M063 3x2-10x+3=0 À«ÄÃPÀgÀtzÀ MAzÀÄ ªÀÄÆ®ªÀÅ 1/3 DVzÉ. E£ÀÆßAzÀÄ ªÀÄÆ®ªÀÅ :

A. 1/3 B. 3 C. 3 1/3 D. 7 1/3

One of the roots of the equation 3x2-10x+3=0 is 1/3. The other root is:

A. 1/3 B. 3 C. 3 1/3 D. 7 1/3 5 S B D

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M064 m ªÀÄvÀÄÛ n UÀ¼ÀÄ x2 -6x +2 =0 JA§ ªÀUÀð ¸À«ÄÃPÀgÀtzÀ ªÀÄÆ®UÀ¼ÁzÀgÉ, PÉ¼ÀV£ÀªÀÅUÀ¼À°è 3PÉÌ ¸ÀªÀÄ£ÁVgÀÄªÀÅzÀÄ? A. m+n B. mn C. m+n D. m2n2

mn

If m and n are the roots of the quadratic equation x2 -6x +2 =0 then 3 is the value of A. m+n B. mn C. m+n D. m2n2

mn 5 S C E

M065 x2-x-c=0 ¸À«ÆPÀgÀtzÀ°è ’c’ AiÀiÁªÀ ¨É ÉAiÀÄÄ, ¸À«ÆPÀgÀtzÀ ªÀÄÆ®UÀ¼ÀÄ ¸ÀA«Ä±Àæ ¸ÀASÉåUÀ¼ÁUÀÄªÀÅªÀÅ?

A. 0 B. -1 C. +1 D. +2

In the equation x2-x-c=0 what value of ’c’ makes the roots of the equation imaginary?

A. 0 B. -1 C. +1 D. +2 5 U C A

M066 FUÀ ªÉÃ¼É 3 UÀAmÉ DVzÀÝgÉ. 48 UÀAmÉUÀ¼À »A¢£À ªÉÃ¼É:

A. 3 UÀAmÉ B. 6 UÀAmÉ C. 9 UÀAmÉ D. 12 UÀAmÉ

At present the time is 3’o’ clock then time before 48 hours was:

A. 3’o’’ clock B. 6’o’ clock C. 9’o’ clock D. 12’o’ clock 6 K A E

M067 2005gÀ ªÀiÁZïð wAUÀ½£À 4 ªÀÄvÀÄÛ 11£ÉÃ ¢£ÁAPÀUÀ¼ÀÄ ±ÀÄPÀæªÁgÀUÀ¼ÁUÀÄvÀÛªÉ. F ¸ÀA§AzsÀªÀ£ÀÄß »ÃUÉ ¥Àæw¤¢ü À§ºÀÄzÀÄ:

A. 4<11 (ªÉÆqï 7) B. 11-4 (ªÉÆqï 7) C. 4>11 (ªÉÆqï 7) D. 4 ≡ 11(ªÉÆqï 7) March 4th and 11th of 2005 are Fridays. This relation can be expressed as:

A. 4<11 (mod 7) B. 11-4 (mod 7) C. 4>11 (mod 7) D. 4 ≡11(mod 7) 6 K D A

M068 Y⊗4 Y = 1 DzÀgÉ, ‘Y’ £À ¸ÀjAiÀiÁzÀ É É :

A. 2 B. 4 C. 5 D. 6

If Y⊗4 Y = 1 then value of ‘Y’ is: A. 2 B. 4 C. 5 D. 6 6 K C E

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M069 2 ⊗5 3 = 1 : : ____ ⊗5 ____ = 1

A. 4, 0 B. 2, 4 C. 3, 4 D. 4, 4

2 ⊗5 3 = 1 : : ____ ⊗5 ____ = 1

A. 4, 0 B. 2, 4 C. 3, 4 D. 4, 4 6 S D E

M070 x+2≡4 (ªÉÆqï 5) DzÁUÀ, ‘x’ £À É ÉAiÀÄÄ

A. 3 B. 4 C. 5 D. 7

If x+2≡4 (mod 5), then the value of ‘x’ is :

A. 3 B. 4 C. 5 D. 7 6 S D E

M071 ( 10⊕ 12 2 ) ⊕ 12 3 AiÀÄ É É :

A. 2 B. 3 C. 10 D. 15

The value of ( 10⊕ 12 2) ⊕ 12 3 is

A. 2 B. 3 C. 10 D. 15 6 S B E

M072 CzsÀðªÀÈvÀÛzÀ°è£À JgÀqÀÄ eÁåUÀ¼À C£ÀÄ¥ÁvÀ 1:1EzÀÝgÉ CªÀÅUÀ¼ÀÄ GAlÄªÀiÁqÀÄªÀ ªÀÈvÀÛ RAqÀUÀ¼À «¹ÛÃtðzÀ C£ÀÄ¥ÁvÀ:

A. 1:1 B. 1:3 C. 2:1 D. 1:3

In a semicircle, the ratio of the length of two chords is 1:1. The ratio of the area of the segments made by them is:

A. 1:1 B. 1:3 C. 2:1 D. 1:3 7 K A E

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M073 avÀæzÀ°è CvÀåAvÀ aPÀÌ ®WÀÄ RAqÀªÀ£ÀÄß ¥ÀqÉAiÀÄ®Ä AiÀiÁªÀ ªÀÈvÀÛ RAqÀPÉÌ §tÚ ºÀZÀÄÑ«j? F E A D A. ABC B. ABD

C. ACDF D. ACDEF B C

In the given figure which segment would you shade to get the smallest minor segment? F E A. ABC B. ABD A D C. ACDF D. ACDEF

B C 7 U A E

M074 ¥ÀgÀ ÀàgÀ bÉÃ¢¸ÀÄªÀ AiÀiÁªÀÅzÉÃ JgÀqÀÄ ªÁå¸ÀUÀ¼À vÀÄ¢©AzÀÄUÀ¼À°è J¼ÉAiÀÄ®àlÖ ¸Àà±ÀðPÀUÀ¼ÀÄ GAlÄªÀiÁqÀÄªÀ DPÀÈwAiÀÄÄ MAzÀÄ:

A. ZÀZËÑPÀ B. DAiÀÄvÁPÁg É C. ÀªÀiÁAvÀgÀ ZÀvÀÄ sÀÄðd D. ZÀvÀÄ sÀÄðd

Tangents drawn at the end points of any two intersecting diameters always form a:

A. Square B. Rectangle C. Parallelogram D. Quadrilateral 7 K D E

O

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M075 avÀæzÀ°è PABQ MAzÀÄ ¸ÀªÀÄ¢é ÁºÀÄ vÁæ¦dåªÁUÀ®Ä F ¸ÀA§AzsÀ«zÁÝUÀ ªÀiÁvÀæ

A B

P D C Q

A. PA ≥ CQ B. PB < CQ C. PD=CQ D. PB>CQ

In the figure PABQ will become an Isosceles trapezium only on the condition:

A B

P D C Q

A. PA ≥ CQ B. PB < CQ C. PD=CQ D. PB>CQ 7 K C E

M076 12 ÉA.«Ä GzÀÝzÀ JgÀqÀÄ ÀªÀiÁ£ÁAvÀgÀ eÁåUÀ¼À£ÀÄß‘x’ ÉA.«Ä CAvÀgÀzÀ°èè ªÀÈvÀÛPÉÃAzÀæzÀ «gÀÄzÀÞ §¢UÀ¼À°è J¼É¢zÉ. DUÀ wædåªÀÅ:

A. √ 144 – x2 B. √36 + x2 C. √36-x2 D. √144-x2 4 4

If two parallel chords of length 12 cm each and x cm apart are drawn on either side of centre then radius of the circle is:

A. √ 144 – x2 B. √36 + x2 C. √36-x2 D. √144-x2 4 4 7 S B E

M077 ABC ªÀÄvÀÄÛ DEF ¸ÀªÀÄgÀÆ¥À wæ¨sÀÄdUÀ¼À C£ÀÄgÀÆ¥À ±ÀÈAUÀUÀ¼ÀÄ A ªÀÄvÀÄÛ D, B ªÀÄvÀÄÛ E ºÁUÀÆ C ªÀÄvÀÄÛ F UÀ¼ÀÄ DVzÀÝgÉ, F PÉ¼ÀV£ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼À eÉÆvÉAiÀiÁVzÉ:

A. AB ªÀÄvÀÄÛ DF B. AC ªÀÄvÀÄÛ DE C. BC ªÀÄvÀÄÛ EF D. AC ªÀÄvÀÄÛ DF Corresponding vertices of two similar triangles ABC and DEF are A & D, B & E, C &F Which of the following pair are corresponding sides of these triangles

A. AB and DF B. AC and DE C. BC and EF D. AC and DF 8 K C E

C1

C2

C1

C2

R

Q

R

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M078 PQR wæ¨sÀÄdzÀ°è ∠PQR = 900, DzÁUÀ, ¸ÀjAiÀiÁzÀ ¸ÀA§AzsÀªÀÅ AiÀiÁªÀÅzÀÄ? ¥ÀvÉÛ ªÀiÁrj: A. PQ 2 = PR 2 + QR 2 B. PR 2 = RP 2 + QR 2

C. PR 2 = PQ 2 + QR 2 D. QR 2 = PR 2 + QP 2 For a triangle PQR where ∠PQR = 900, which is the correct relation among the following A. PQ 2 = PR 2 + QR 2 B. PR 2 = RP 2 + QR 2

C. PR 2 = PQ 2 + QR 2 D. QR 2 = PR 2 + QP 2 8 K C E

M079 MAzÀÄ ®A§PÉÆÃ£ wæ¨sÀÄdzÀ ¨ÁºÀÄUÀ¼À C£ÀÄ¥ÁvÀªÀÅ 3:4:5 F ÀA§AzsÀªÀ£ÀÄß UÀªÀÄ£ÀzÀ°èlÄÖPÉÆAqÀÄ, ©nÖgÀÄªÀ ¥ÀzÀªÀ£ÀÄß vÀÄA©¹ 5:12: ----- A. 19 B. 13 C. 17 D. 24 If the sides of a right-angled triangle are in the ratio 3:4:5 then the missing term in 5:12: ------ is: A. 19 B. 13 C. 17 D. 24 8 U B E

M080 F avÀæzÀ°ègÀÄªÀ ¥ÀgÁåAiÀÄ PÉÆÃ£ÀUÀ¼À eÉÆvÉAiÀÄ£ÀÄß ¥ÀvÉÛ ªÀiÁrj: A. ∟PRQ & ∟MRN B. ∟QPR & ∟RMN C. ∟PQR & ∟NMR D. ∟RPQ & ∟RMN In the given figure pair of alternate angles is A. ∟PRQ & ∟MRN B. ∟QPR & ∟RMN C. ∟PQR & ∟NMR D. ∟RPQ & ∟RMN 8 U C E

M

P

N

Q R

M

P

Q

N R

A

B C

P Q

A

B C

P Q

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M081 avÀæzÀ ÀºÁAiÀÄ¢AzÀ ¥ÀÆtð ªÀiÁrj:

Complete the statement using the given figure

8 K C E

M082 avÀæªÀ£ÀÄß £ÉÆÃr ¸ÀjAiÀiÁzÀ ¸ÀA§AzsÀÀªÀ£ÀÄß ¥ÀvÉÛ ªÀiÁrj:

A. AP.AB = AQ.AC

B. AP.AC = AQ.AB

C. AP.AQ = AC.AB

D. AP.PQ = BC.AC

Which is the correct relation among the following

A. AP.AB = AQ.AC

B. AP.AC = AQ.AB

C. AP.AQ = AC.AB

D. AP.PQ = BC.AC 8 U A A

AB : AQ : : BC : ______

A. AQ B. AP C. PQ D. AC

AB : AQ : : BC : ______

A. AQ B. AP C. PQ D. AC

P Q

P Q

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M083 JgÀqÀÄ ¸ÀªÀÄgÀÆ¥À wææ sÀÄdUÀ¼À «¹ÛÃtðªÀÅ 392 ZÀ.¸ÉA.«Ä ªÀÄvÀÄÛ 200ZÀ. ÉA.«Ä CªÀÅUÀ¼À C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼À C£ÀÄ¥ÁvÀªÀÅ

A. 3:2 B. 49:25 C. 7:5 D. 14:10 Two similar triangles have areas 392 sq cm and 200 sq.cm respectively; What is the ratio of any pair of corresponding sides.

A. 3:2 B. 49:25 C. 7:5 D. 14:10 8 U C A

M084 MAzÀÄ ªÀÈvÀÛzÀ ªÁå¸ÀPÉÌ ¸ÀA§AzsÀ«®èzÀAvÀºÀ ºÉÃ½PÉAiÀÄÄ:

A. ªÀÈvÀÛzÀ wædåzÀ JgÀqÀgÀµÀÄÖ B. ªÀÈvÀÛzÀ CvÀåAvÀ zÉÆqÀØ eÁå

C. ªÀÈvÀÛªÀ£ÀÄß JgÀqÀÄ CzsÀðªÀÈvÀÛUÀ¼ÁV C¢üð¸ÀÄvÀÛzÉ D. MAzÀÄ ¸ÀgÀ¼ÀgÉÃSÉ The statement not related to the diameter of a circle is:

A. twice the radius of the circle B. longest chord of the circle

C. bisects the circle into two semicircles D. a straight line 8 K D E

M085 ¨ÁºÀåªÁV ¸Àà²ð¸ÀÄªÀ ªÀÈvÀÛUÀ½UÉ ¸ÀA§A¢ü¹zÀ ¸À«ÄÃPÀgÀtªÀ£ÀÄß ¥ÀvÉÛªÀiÁr:

A. d>R+r B. d = R + r C. d < R + r D. d = R - r Which relation among the following refers to externally touching circles:

A. d>R+r B. d = R + r C. d < R + r D. d = R – r 8 K B E

M086 JgÀqÀÄ wæ sÀÄdUÀ¼ÀÄ ¸ÀªÀÄPÉÆÃ¤AiÀÄUÀ¼ÁVzÀÝgÉ, CªÀÅUÀ¼À C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼ÀÄ:

A. ¸ÀªÀÄ B. ¸ÀªÀiÁ£ÁAvÀgÀ C. ®A§ D. ¸ÀªÀiÁ£ÀÄ¥ÁvÀ If two triangles are equiangular, then their sides are: A. equal B. parallel C. perpendicular D. proportional 8 U D E

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M087 JgÀqÀÄ ¸ÀªÀiÁAvÀgÀªÁVgÀÄªÀ ¸Àà±ÀðPÀUÀ¼À £ÀqÀÄ«£À, MAzÀÄ Àà±ÀðPÀ bÉÃzÀPÀªÀÅ ªÀÈvÀÛ PÉÃAzÀæzÀ°è PÉÆÃ£ÀªÀ£ÀäßAlÄªÀiÁqÀÄvÀÛzÉ. D PÉÆÃ£ÀzÀ C¼ÀvÉAiÀÄÄ: A. ®WÀÄ B. ®A§ C. C¢üPÀ D. ¸ÀgÀ¼À The intercept of a tangent between two parallel tangents to a circle subtends an angle at the centre. The measure of the angle is: A. acute B. right C. obtuse D. straight 8 U B A

M088 MAzÀÄ ¥Áè¹ÖPï WÀ£À UÉÆÃ¼ÀªÀ£ÀÄß PÀgÀV¹, MAzÀÄ UÉÆA ÉAiÀÄ£ÀÄß ªÀiÁrzÁUÀ CzÀgÀ°è §zÀ ÁUÀzÉ EgÀÄªÀÅzÀÄ A. DPÁgÀ B. GzÀÝ C. ªÉÄÃ¯ÉäöÊ«¹ÛÃtð D. WÀ£À¥sÀ®À A solid plastic sphere is melted and a doll is made. There will be no change in its: A. shape B. length C. area D. volume 9 K D E

M089 PÉÆnÖgÀÄªÀ ¹°AqÀj£À°è, JgÀqÀÄ ©AzÀÄUÀ¼À £ÀqÀÄ«£À CvÀåAvÀ zÀÆgÀ :

A o D A. AB B. AD C. AC D. OC B C

The farthest distance between the two points on the given cyclinder:

A o D A. AB B. AD C. AC D. OC B C 9 U C E

O

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M090 MAzÀÄ CzsÀðªÀÈvÁÛPÁgÀzÀ ¯ÉÆÃºÀzÀ ºÁ¼ÉAiÀÄ£ÀÄß, MAzÀÄ vÉgÀzÀ ±ÀAPÀ«£À §lÖ® DPÁgÀzÀ°è §VÎ¹zÉ. DUÀ CzsÀðªÀÈvÀÛzÀ ªÁå¸ÀªÀÅ EzÀPÉÌ DUÀÄvÀÛzÉ.

A. §lÖ°£À ¥Àj¢ü B. §lÖ°£À NgÉ JvÀÛgÀ

C. §lÖ°£À D¼À D. §lÖ°£À ªÁå¸À

A semicircular sheet of a metal is bent into an open conical cup. The diameter of the semicircle becomes:

A. Circumference of the cup B. Slant height of the cup

C. Depth of the cup D. Diameter of the cup 9 U B E

M091 MAzÀÄ ¹°AqÀgÁPÁgÀzÀ ¥É¤ß£À°è, MAzÀÄ ¨Áj ªÀÄ¹ vÀÄA©zÁUÀ, 22 ¥ÀÄlUÀ¼ÀµÀÄÖ §gÉAiÀÄ§ºÀÄzÀÄ. 100 cc ªÀÄ¹¬ÄAzÀ 1600 ¥ÀÄlUÀ¼ÀÄ §gÉAiÀÄ§ºÀÄzÀÄ. ¥É¤ß£À AiÀiÁªÀ C¼ÀvÉAiÀÄ£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä F zÀvÁÛA±ÀªÀÅ ¸ÀºÁAiÀÄPÀªÁVzÉ?

A. «¹ÛÃtð B. ¥sÀ£À¥sÀ® C. JvÀÛgÀ D. wædå

A cylindrical fountain pen, when filled with ink can be used to write 22 pages. With 100 cc of ink. 1600 pages can be written. Which of the following measures can we find through this data?

A. area B. volume C. height D. radius 9 U B E

M092 6¸ÉA.«Ä wædåªÀÅ¼Àî vÁªÀÄæzÀ UÉÆÃ¼ÁPÁgÀzÀ UÀÄAqÀ£ÀÄß PÀgÀV¹zÉ ªÀÄvÀÄÛ CzÀ£ÀÄß 0.06 æ ¸ÉA.«Ä wæædå«gÀÄªÀ vÀAwAiÀÄ£ÁßV J¼É¢zÉ. vÀÀAwAiÀÄ GzÀÝªÀÅ :

A. 600 «Æ B. 650 «Æ C. 800 «Æ D. 825 «Æ

A copper sphere of radius 6 cms is melted and drawn into a wire of radius 0.06 cm. The length of the wire is:

A. 600 m B. 650 m C. 800 m D. 825 m 9 S C A

M093 MAzÀÄ UÉÆÃ¼ÀzÀ WÀ£À¥sÀ® ªÀÄvÀÄÛ ªÉÄÃ¯ÉäöÊ «¹ÛÃtðUÀ¼ÀÄ ¯ÉPÁÌZÁgÀ ¥ÀæPÁgÀ MAzÉÃ DVzÁÝUÀ, CzÀgÀ ªÁå¸ÀªÀÅ:

A. 3 KPÀªÀiÁ£ÀUÀ¼ÀÄ B. 6 KPÀªÀiÁ£ÀUÀ¼ÀÄ C. 8 KPÀªÀiÁ£ÀUÀ¼ÀÄ D. 9 KPÀªÀiÁ£ÀUÀ¼ÀÄ

If the volume and surface area of a sphere are numerically equal, then, its diameter is :

A. 3 units B. 6 units C. 8 units D. 9 units 9 U A A

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M094 7 «Ælgï ªÁå¸À ªÀÄvÀÄÛ 5 «Ælgï GzÀÝªÀÅ¼Àî MAzÀÄ gÉÆÃ®gï ªÉÄÊzÁ£ÀzÀ°è GgÀÄ½ À ÁVzÉ. gÉÆÃ®gï ªÀiÁrzÀ ¸ÀÄvÀÄÛUÀ¼À ¸ÀASÉåAiÀÄ£ÀÄß PÀAqÀÄ»rAiÀÄ®Ä ÉÃPÁzÀ zÀvÁÛA±ÀªÀÅ :

A. gÉÆÃ®gï£À MlÄÖ ªÉÄÃ¯ÉäöÊ «¹ÛÃtð B. CzÀgÀ ªÀPÀæ ªÉÄÃ¯ÉäöÊ«¹ÛÃtð

C. gÉÆÃ®gï£À ¸ÀªÀÄvÀlÄÖ ªÀiÁrzÀ GzÀÝ D. gÉÆÃ®gï£À WÀ£À¥sÀ®

A roller of 5 m length and 7 m diameter, rolled on a field. To find the number of revolutions it makes, data required is :

A. Total surface area of the roller B. Curved surface area of the roller

C. Total length covered by the roller D. Volume of the roller 9 U C A

M095 ªÉÄÃ¯ÉäöÊUÀ¼À ¸ÀASÉå ªÀÄvÀÄÛ ±ÀÈAUÀUÀ¼À ¸ÀASÉåUÀ¼ÀÄ AiÀiÁªÁUÀ®Æ MAzÉÃ ¸ÀªÀÄ£ÁVgÀÄªÀ ¥sÀ£ÀªÀÅ:

A. óµÀtÄäRWÀ£À B. ¥ÀlÖPÀ C. UÉÆÃ¥ÀÄgÀ D. ¥ÁèmÉÆÃ¤Pï WÀ£À

The solid in which number of faces are always equal to the number of vertices is:

A. Hexahedron B. Prism C. Pyramid D. Platonic solid 10 K C A

M096 F PÉ¼ÀV£ÀªÀÅUÀ¼À°è AiÀiÁªÀÅzÀÄ ÇÁzÀå A. ªÀÄÆgÀÄ ¸ÀA¥ÁvÀ ©AzÀÄUÀ¼À vÁgÀªÁºÀPÀ eÁ¯ÁPÀÈw gÀd£É B. JgÀqÀÄ ¨É À ¸ÀA¥ÁvÀ ©AzÀÄUÀ¼À ¥ÁgÀªÁºÀPÀ eÁ¯ÁPÀÈw gÀZÀ£É C. MAzÀÄ ¨É À ¸ÀA¥ÁvÀ ©ªÀÄzÀÄ«gÀÄªÀ eÁ¯ÁPÀÈw gÀZÀ£É D. JgÀqÀÄ ¨É À ¸ÀA¥ÁvÀ ©AzÀÄ«gÀÄªÀ eÁ¯ÁPÀÈw gÀZÀ£É Which one of the following is impossible to do? A. drawing a traversable network of 3 nodes B. making a traversable network of 2 odd nodes C. drawing a network of one odd node D. drawing a network of two odd nodes 10 A C E

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M097 F eÁ¯ÁPÀÈwAiÀÄ ªÀiÁvÀÈPÉAiÀÄ°è JµÀÄÖ ÀÄgÀÄ½UÀ½ªÉ:

0 1 2

1 4 3

2 3 0

A. 1 B. 2 C. 3 D. 4

How many loops are there in the network of matrix?

0 1 2

1 4 3

2 3 0

A. 1 B. 2 C. 3 D. 4 10 K B E

M098 F WÀ£ÁPÀÈwAiÀÄ£ÀÄß ºÉ Àj¹:

A. ªÀUÀð¥ÁzÀ UÉÆÃ¥ÀÄgÀ B. ªÀUÀð¥ÁzÀ ¥ÀlÖPÀÉ

C. wæ sÀÄd¥ÁzÀ ¥ÀlÖPÀ D. ¤AiÀÄ«ÄvÀ µÀtÄäR WÀ£À

Name the polyhedra

A. square based pyramid B. square based prism

C. triangular prism D. regular hexahedron

10 K B E

A

B

C

D

A

B

C

D

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No.

Questions

Ch.No Obj Key

Diff.

level

M099 F eÁ¯ÁPÀÈwAiÀÄÄ ¥ÁgÀªÁºÀPÀÀ eÁ¯ÁPÀÈwAiÀÄ®è AiÀiÁPÉAzÀgÉ: A. PÉÃªÀ® 4 ¸ÀA¥ÁvÀ ©AzÀÄUÀ½ªÉ B. JgÀqÀÄ ¨É À ¸ÀA¥ÁvÀ ©AzÀÄUÀ½ªÉ C. J¯Áè ÀA¥ÁvÀ ©AzÀÄUÀ¼ÀÄ ÀªÀÄ ¸ÀA¥ÁvÀ ©AzÀÄUÀ¼ÀÄ D. JgÀqÀQÌAvÀ ºÉZÀÄÑ É À ¸ÀA¥ÁvÀ ©AzÀÄUÀ½ªÉ The given network is not a traversable network because: A. there are 4 nodes B. there are two odd nodes C. all nodes are even nodes D. there are more than two odd nodes

10 U D E

M100 F PÉ¼ÀV£À avÀæªÀ£ÀÄß CzÀgÀ vÀÄ¢UÀ¼À°è ªÀÄrazÁUÀ GAmÁUÀÄªÀ ¤AiÀÄ«ÄvÀ §ºÀÄ ¥À®PÀªÀ£ÀÄß ºÉ Àj¹:

A. ZÀvÀÄðªÀÄÄR WÀ£À B. µÀtÄäR WÀ£À

C. CµÀÖªÀÄÄR WÀ£ D. zÁézÀ±ÀªÀÄÄR WÀ£À

Name the regular polyhedron can be formed by folding the given structure at its edges A. Tetrahedron B. Hexahedron C. Octahedron D. Dodecahedron 10 A B E

A

A

D.S.E.R.T #4, 100 fT ring road, Banashankari III stage, Bangalore – 85

Subject : Mathematics sÁUÀ II £ÀÄß GvÀÛj ÀÄªÀÅzÀPÉÌ ÀÆZÀ£É

Instructions for answering Part II

PÉ¼ÀV£À ¥Àæ±ÉßUÀ¼À£ÀÄß, ÀÆZÀ£ÉUÀ½UÉ vÀPÀÌAvÉ GvÀÛj¹: Answer the following question as directed:

Item

No. Questions Ch.No Obj Marks Diff.

Level

M001 MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ ªÉÆzÀ®£É ªÀÄvÀÄÛ 129£ÉÃ ¥ÀzÀUÀ¼ÀÄ PÀæªÀÄªÁV 2 ªÀÄvÀÄÛ 258 DVªÉ. 65£ÉÃ ¥ÀzÀªÀ£ÀÄß PÀAqÀÄ »r¬Äj.

First and the 129th term of an A.P are respectively 2 and 258. Find the 65th term

1 K,S 1+1 E

M002 MAzÀÄ UÀÄuÉÆÃvÀÛgÀ ±ÉæÃrüAiÀÄ°è Tn-1 = 1 JAzÀÄ vÉÆÃj¹. Tn+1 r

2 In a G.P show that Tn-1 = 1 Tn+1 r

2

1 K,U 1+1 A

M003 MAzÀÄ ZËPÀªÀ£ÀÄß 16 aPÀÌ ZÀzÀgÀUÀ¼ÁV sÁUÀªÀiÁrzÉ. M§â ºÀÄqÀÄUÀ£ÀÄ, ªÉÆzÀ®£É ZËPÀzÀ°è 2 UÉÆÃ°UÀ¼À£ÀÄß ªÀÄvÀÄÛ CzÀgÀ ªÀÄÄA¢£À ZËPÀzÀ°è 4 UÉÆÃ°UÀ¼À£ÀÄß EqÀÄvÁÛ£É. »ÃUÉAiÉÄÃ ¥Àæw ¸À®ªÀÅ 2 UÉÆÃ°UÀ¼À£ÀÄß ºÉaÑ ÀÄvÁÛ ªÀÄÄAzÀÄªÀj¸ÀÄªÀ£ÀÄ. J¯Áè ZËPÀUÀ¼À£ÀÄß vÀÄA§®Ä CªÀ¤UÉ MlÄÖ JµÀÄÖ UÉÆÃ°UÀ¼ÀÄ ÉÃPÁUÀÄªÀÅzÀÄ?

A square is divided into 16 smaller squares. A boy keeps 2 marbles in the first square, 4 in the next, and continues by increasing 2 marbles each time. How many marbles are needed to fill all the squares?

1 U,S 1+1 A

M004 ªÀÄÆgÀÄ KPÀPÉÃA¢æAiÀÄ ªÀÈvÀÛUÀ¼À wædåUÀ¼À C£ÀÄ¥ÁvÀªÀÅ MAzÉÃ ¸ÀªÀÄ¥ÁvÀzÀ°ègÀÄªÀAvÉ J¼É¢zÉ. M¼ÀV£À ªÀÄvÀÄÛ CvÀåAvÀ ºÉÆgÀV£À ªÀÈvÀÛUÀ¼À wædåUÀ¼ÀÄ PÀæªÀÄªÁV 3 ¸ÉA.«Ä , 12 ¸ÉA.«Ä DVªÉ. ªÀÄzsÀåzÀ ªÀÈvÀÛzÀ wdåªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

Three concentric circles are drawn in such a way that the ratio of their radii is same. If the radii of the inner and outer circles are 3 cms and 12 cms respectively. Find the radius of the middle circle.

1 A,S 1+1 A

M005 1, 2, 3, 4 ªÀÄvÀÄÛ 5 CAPÉUÀ¼À£ÀÄß G¥ÀAiÉÆÃV¹PÉÆAqÀÄ, ¥ÀÄ£ÀgÁªÀwð¸ÀzÉ, 2000PÀÆÌ ºÉaÑgÀÄªÀAvÉ JµÀÄÖ ¸ÀASÉåUÀ¼À£ÀÄß ªÀiÁqÀ§ºÀÄzÀÄ?

How many numbers, more than 2000 can be formed using digits 1, 2, 3, 4 and 5 without repeating the digits? 2 K,S 1+1 E

Item


Level

M006 10 d£ÀgÀ JvÀÛgÀ ªÀÄvÀÄÛ vÀÆPÀUÀ¼À, ÀgÁ Àj ªÀÄvÀÄÛ ªÀiÁ£ÀPÀ «ZÀ®£ÉAiÀÄ£ÀÄß PÉ¼ÀV£À ¥ÀnÖAiÀÄ°è PÉÆqÀ ÁVzÉ. CªÀgÀ AiÀiÁªÀ ®PÀëtªÀÅ ºÉZÀÄÑ C¹ÜgÀªÁVzÉ?

UÀÄt®PÀët X ൦

JvÀÛgÀ 174 ÉA.«Ä 3.77

vÀÆPÀ 75 PÉ.f 1.05

The table below contains the mean and standard deviation of the heights and weights of 10 persons. In which characteristic do they vary more?

Characteristic X ൦

Height 174 cms 3.77

Weight 75 Kg 1.05 3 K,S 1+1 E

Item


Level

M007 ÉÃgÉ ÉÃgÉ PÀ ÀÄ§ÄUÀ¼À°è£À d£ÀgÀ UÀÄA¥ÀÄ, MAzÀÄ ¤UÀ¢üvÀ CªÀ¢üAiÀÄ°è UÀ½¹zÀ ¢£ÀUÀÆ°AiÀÄ, ªÀiÁ£ÀPÀ«ZÀ®£ÉAiÀÄ£ÀÄß ¯ÉPÁÌZÁgÀ ªÀiÁr, £ÀPÉëAiÀÄ°è vÉÆÃj¹zÉ. AiÀiÁªÀ UÀÄA¦£À d£ÀgÀ PÀÆ°AiÀÄÄ ¹ÜgÀªÁVzÉ?

0

1

2

3

4

5

6

7

8

9

10

Carpenter Coolie Driver Painter Plumber

Occupations

S.D's of wages

Following graph shows the calculated S.D’s of wages of groups of people of different occupations for a certain period. Which group of people have a steady income?

0

1

2

3

4

5

6

7

8

9

10

Carpenter Coolie Driver Painter Plumber

Occupations

S.D's of wages

3 A 2 A

M008 a2-b2, (a-b)2 ªÀÄvÀÄÛ a3-b3 UÀ¼À ªÀÄ.¸Á.ªÀ £ÀÄß PÀAqÀÄ »r¬Äj:

Find the H.C.F of a2-b2, (a-b)2 and a3-b3 4 S 2 E

M009 x+y+z=9 ªÀÄvÀÄÛ xy+yz+zx=11 DzÁUÀ x3+y3+z3-3xyz É ÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

When x+y+z=9 and xy+yz+zx=11, find the value of x3+y3+z3-3xyz 4 K,S 1+1 A

Item


Level

M010 JgÀqÀÄ ©ÃeÉÆÃQÛUÀ¼À ªÀÄ.¸Á.C ªÀÄvÀÄÛ ®.¸Á.C UÀ¼ÀÄ PÀæªÀÄªÁV (x-3) ªÀÄvÀÄÛ (x3-5x2-2x+24)DVªÉ. CªÀÅUÀ¼À°è MAzÀÄ ©ÃeÉÆÃQÛAiÀÄÄ (x2-7x+12) DzÀgÉ, ªÀÄvÉÆÛAzÀ£ÀÄß PÀAqÀÄ»r¬Äj.

The H.C.F and L.C.M of two expressions are (x-3) and (x3-5x2-2x+24) respectively. If one of the expressions is (x2-7x+12), find the other 4 U,S 1+1 A

M011 2x2-3x+8=0 ¸À«ÆPÀgÀtzÀ ªÀÄÆ®UÀ¼À §UÉÎ «ªÀÄ²ð¹:

Comment on the roots of the equation: 2x2-3x+8=0 5 K 2 E

M012 MAzÀÄ ªÀUÀð¸À«ÆPÀgÀtzÀ ±ÉÆÃzsÀPÀzÀ ¨É É 16 DzÀgÉ, ªÀUÀð¸À«ÆPÀgÀtzÀ ªÀÄÆ®UÀ¼À ¸Àé sÁªÀªÉÃ£ÀÄ?

If the value of the discriminant of a quadratic equation is 16. What is the nature of the roots of the equation? 5 K,S 1+1 E

M013 ªÀÄÆ®UÀ¼ÀÄ (1-√5) ªÀÄvÀÄÛ (1+√5) EgÀÄªÀAvÉ MAzÀÄ ªÀUÀð¸À«ÄÃPÀgÀtªÀ£ÀÄß §gÉ:

Write the quadratic equation whose roots are (1-√5) and (1+√5) 5 K,S 1+1 E

M014 (6�87 ) �85 = 6�8 (7� 85)JAzÀÄ vÉÆÃj¹:

Show that (6�87 ) �85 = 6�8 (7� 85) 6 K.S 1+1 A

M015 Z4 UÀÄuÁPÁgÀPÉÌ ¸ÀA§A¢ü¹zÀAvÉ PÉÆÃµÀ×PÀªÀ£ÀÄß gÀa¸À®Ä ¸ÁzsÀåªÉÃ? PÁgÀt w½¹

� 2 4 6 8

2 4 8 2 6 4 8 6 4 2 6 2 - - - 8 6 - - -

Check whether construction of Cayley’s table is possible for Z4 under multiplication. State the reason � 2 4 6 8

2 4 8 2 6 4 8 6 4 2 6 2 - - - 8 6 - - - 6 U 2 A

Two congruent circles with centers A and B of 2 cm radius, touch two other congruent circles with centers C and D of radius 4 cm as shown in the figure. Find the perimeter of the rectangle ABCD

Item


Level

M016

7 U 2 A

M017

7 U 2 A

M018

8 U,S 1+1 A

4¸ÉA.«Ä wædå«gÀÄªÀ £Á®ÄÌ ¸ÀªÀð¸ÀªÀÄ ªÀÈvÀÛUÀ¼À PÉÃAzÀæUÀ¼ÀÄ A, B, C ªÀÄvÀÄÛ D DVªÉ. F ªÀÈvÀÛUÀ¼ÀÄ avÀæzÀ°è vÉÆÃj¹gÀÄªÀAvÉ MAzÀ£ÉÆßAzÀÄ ¸Àà²ð¸ÀÄwÛªÉ. ABCD ZËPÀzÀ «¹ÛÃtðªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

Four circles of radius 4 cm with centers A, B, C and D touch each other as shown in the figure. Find the perimeter of the square ABCD

A ªÀÄvÀÄÛ B PÉÃAzÀæªÁUÀÄ¼Àî JgÀqÀÄ ¸ÀªÀð¸ÀªÀÄ ªÀÈvÀÛUÀ¼À wædå 2 ¸ÉA.«Ä DVzÉ. F JgÀqÀÄ ªÀÈvÀÛUÀ¼À, 4 ¸ÉA.«Ä wædå«gÀÄªÀ C ªÀÄvÀÄÛ D PÉÃAzÀæUÀ¼ÁVgÀÄªÀ, JgÀqÀÄ ¸ÀªÀð¸ÀªÀÄ ªÀÈvÀÛUÀ¼À£ÀÄß avÀæzÀ°èè vÉÆÃj¹zÀAvÉ ¸Àà²ð¸ÀÄwÛªÉ. DAiÀÄvÀ ABCDAiÀÄ ¸ÀÄvÀÛ¼ÉAiÀÄ£ÀÄß ÉQÌ¹.

avÀæzÀ°è AP ªÀÄvÀÄÛ BP UÀ¼ÀÄ ªÀÈvÀÛzÀ PÉÃAzÀæªÀÅ O ªÀÄvÀÄÛ ¨ÁºÀå ©AzÀÄ P ¤AzÀ

J¼É¢gÀÄªÀ ¸Àà±ÀðPÀUÀ¼ÀÄ, ∠APB=700 DzÀgÉ PÉÆÃ£À ∠ACB AiÀÄ É ÉAiÉÄÃ£ÀÄ?

In the adjoining figure AP and BP are tangents drawn to the circle with

centre O from an external point P. If ∠APB=700, Find ∠ACB

Item


Level

M019 F avÀæzÀ°è CAvÀ:¸ÀÜªÁV ¸Àà²ð¸ÀÄªÀ ªÀÈvÀÛUÀ¼À eÉÆvÉ JµÀÄÖ?

In the adjoining figure how many pairs of internally touching circles are there?

8 U 2 A

M020 APB ªÀÈvÀÛzÀ°è AB AiÀÄÄ ªÁå¸ÀªÁVzÉ. AH ªÀÄvÀÄÛ BK UÀ¼ÀÄ PÀæªÀÄªÁV A ªÀÄvÀÄÛ B ©AzÀÄUÀ½AzÀ, P ¬ÄAzÀ J¼ÉzÀ ¸Àà±ÀðPÀPÉÌ ®A§UÀ¼ÁVªÉ. AH + BK = AB JAzÀÄ ¸Á¢ü¹.

AB is a diameter of a circle APB. AH and BK are perpendiculars from A and B respectively to the tangent at P. Prove that, AH + BK = AB 8 U,A 1+1 A

M021

8 K,A 1+1 A

M022 7«Æ. ªÁå¸À ªÀÄvÀÄÛ 20«Ælgï D¼À«gÀÄªÀ MAzÀÄ ¨Á«AiÀÄ£ÀÄß CUÉ¢zÉ. CzÀjAzÀ zÉÆgÉvÀ ªÀÄtÚ£ÀÄß ¸ÀªÀÄªÁV ºÀgÀr 22«Æ x 14«Æ C¼ÀvÉAiÀÄ MAzÀÄ dUÀÄ°AiÀÄ£ÀÄß ªÀiÁrzÉ. dUÀÄ°AiÀÄ JvÀÛgÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

A well of diameter 7 m and depth 20 m is dug. The mud obtained is spread uniformly to form a platform measuring 22m x 14 m. Find the height of the platform. 9 U,A 1+1 A

avÀæzÀ°è AB || DC JAzÀÄ PÉÆnÖzÁÝUÀ, Δ DMU ||| Δ BMV JAzÀÄ ¸Á¢ü¹

In the figure, give that AB || DC,

Prove that Δ DMU ||| Δ BMV

Item


Level

M023 10¸ÉA.«Ä JvÀÛgÀ ªÀÄvÀÄÛ 6 ¸ÉA.«Ä ªÁå¸À«gÀÄªÀ MAzÀÄ WÀ£À ¹°AqÀgÀ£ÀÄß PÀgÀV¹, £ÁtåUÀ¼À£ÀÄß ªÀiÁqÀ ÉÃPÁVzÉ. ¥Àæw £ÁtåzÀ ªÁå¸ÀªÀÅ 1.5 ¸ÉA,«Ä ªÀÄvÀÄÛ 0.25 ÉA.«Ä zÀÀ¥Àà«gÀÄªÀAvÉ JµÀÄÖ £ÁtåUÀ¼À£ÀÄß ªÀiÁqÀ§ºÀÄzÀÄ?

A solid cylinder of height 10 cm and diameter 6 cm is melted to make coins. How many coins can be made of diameter 1.5cm with 0.25 cm thickness? 9 K,A 1+1 A

M024 MAzÀÄ ±ÀAPÀÄDPÁgÀzÀ UÀÄqÁgÀzÀ°è 4 d£ÀjgÀ®Ä CªÀPÁ±À«zÉ. ¥ÀæwAiÉÆ§â¤UÀÆ, £É®zÀ ªÉÄÃ¯É 4WÀ.«Æ £ÀµÀÄÖ UÁ½ ÉÃPÁUÀÄvÀÛzÉ. UÀÄqÁgÀzÀ JvÀÛgÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj.

A conical tent accommodates 4 persons. Each person requires 4 sq.m of space on the ground and 20 cu.m of air. Find the height of the tent. 9 A,S 1+1 D

M025

.

.

10 K,S 1+1 A

zÁézÀ±ÀÀªÀÄÄR WÀ£ÀzÀ ªÀÄÄRUÀ¼À ¸ÀASÉå, ±ÀÈAUÀ©AzÀÄUÀ¼À ¸ÀASÉå ªÀÄvÀÄÛ CAZÀÄUÀ¼À ¸ÀASÉåUÀ¼À£ÀÄß JtÂ¹ §gÉ¬Äj. EªÀÅUÀ¼À£ÀÄß DAiÀÄè®gÀ£À ¸ÀÆvÀæzÀ C£ÀéAiÀÄ vÁ¼É £ÉÆÃr.

Write the number of faces, vertices and edges of the given Dodecahedron and verify Euler’s formula

Item


Level

M026 MAzÀÄ eÁ¯ÁPÀÈwAiÀÄ ªÀiÁUÀð ¸ÀASÁåAiÀÄvÀªÀ£ÀÄß PÉÆnÖzÉ. eÁ¯ÁPÀÈwAiÀÄ£ÀÄß gÀa¸ÀzÉ CzÀgÀ°ègÀÄªÀ PÀA¸ÀUÀ¼À ¸ÀASÉåAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0

The network matrix of a network is as follows. Find the number of arcs present in the network without constructing the network.

0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0

10 K,U 1+1 A

M027 PÉ¼ÀV£À avÀæPÉÌ DAiÀÄègÀ£À ¸ÀÆvÀæ C£Àé¬Ä¹ vÁ¼É£ÉÆÃqÀ®Ä ¸ÁzsÀå«®è, PÁgÀt w½¹: A B

D C

It is not possible to verify Euler’s formula for the diagram given below. Give reason: A B

D C 10 U 2 A

E

E

Item


Level

M028 MAzÀÄ ¸ÀªÀiÁAvÀgÀ ±ÉæÃrüAiÀÄ 4£ÉÃ ªÀÄvÀÄÛ 7£ÉÃ ¥ÀzÀUÀ¼ÀÄ PÀæªÀÄªÁV ªÀÄvÀÄÛ 23 DVªÉ. ‘d’ ªÀÄvÀÄÛ ‘a’.UÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.

In an A.P the fourth and the seventh terms are 17 and 23 respectively. Find ‘d’ and ‘a’. 1 K,S 1+2 E

M029 n=7 ªÀÄvÀÄÛ r=3 DzÀgÉ nCr+nCr-1 = n+1Cr JAzÀÄ vÉÆÃj¹.

If n=7 and r=3 show that nCr+nCr-1 = n+1Cr 2 U,S 2+1 E

M030 A ªÀÄvÀÄÛ B JA§ E§égÀÄ ¨ÁålìªÀÄ£ïUÀ¼ÀÄ DgÀÄ E¤ßAUïUÀ¼À°è UÀ½¹gÀÄªÀ gÀ£ÀÄßUÀ¼À «ªÀgÀ »ÃVzÉ:

A 48 50 54 46 48 54

B 46 44 43 46 45 46

EªÀgÀ°è: (a) GvÀÛªÀÄ g£Áß UÀ½¹zÀªÀ AiÀiÁgÀÄ (b) ºÉaÑ£À ¹ÜgÀvÉAiÀÄÄ¼Àî DlUÁgÀ£ÁgÀÄ?

The runs scored by two Batsman A and B in six innings are given as follows:

A 48 50 54 46 48 54

B 46 44 43 46 45 46

Find: (a) who is a better run getter (b) who is a consistent player? 3 U,A 1+2 A

M031 JgÀqÀ£ÉÃ WÁvÀzÀ JgÀqÀÄ ©ÃeÉÆÃQÛUÀ¼À ªÀÄ.¸Á.C ªÀÄvÀÄÛ ®.¸Á.C UÀ¼ÀÄ PÀæªÀÄªÁV (p+2) ªÀÄvÀÄÛ p3-2p2-5p+6. MAzÀÄ ©ÃeÉÆÃQÛ p2+p-2 DzÀgÉ E£ÉÆßAzÀÄ ©ÃeÉÆÃQÛAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj.

HCF and LCM of two expressions of second degree are (p+2) and p3-2p2-5p+6 respectively. If one of the expressions is p2+p-2. Find the other. 4 K,S 1+2 A

M032 a3+7b3+6ab (a+2b) : ©ÃeÉÆÃQÛAiÀÄ£ÀÄß ¤ªÀÄUÉ w½¢gÀÄªÀ MAzÀÄ ¸ÀÆvÀæ gÀÆ¥ÀPÉÌ vÀAzÀÄ, C¥ÀªÀwð¹.

Factorise a3+7b3+6ab (a+2b) by reducing the expression to a known formula 4 U,S 2+1 A

M033 UÀÄt®§Þ 224£ÀÄß PÉÆqÀÄªÀ JgÀqÀÄ PÀæªÀiÁ£ÀÄUÀvÀ zsÀ£À¥ÀÆtð ¸Àj¸ÀASÉåUÀ¼À£ÀÄß PÀAqÀÄ»r¬Äj.

Find two consecutive positive even integers whose product is 224 5 U,S 1+2 E

M034 JgÀqÀÄ ¸ÀªÀÄ wædåUÀ½gÀÄªÀ ªÀÈvÀÛUÀ½UÉ £ÉÃgÀ ÁªÀiÁ£Àå ¸Àà±ÀðUÀ¼À£Éß¼É¬Äj.

Draw the direct common tangents to two equal circles 7 A,S 1+2 A

Item


Level

M035 2 ÉA.«Ä wædå«gÀÄªÀ MAzÀÄ ªÀÈvÀÛ J¼ÉzÀÄ, CzÀgÀ wædå OB AiÀÄ£ÀÄß BX=2 ÉA,«Ä EgÀÄªÀAvÉ ªÀÈ¢Þ¹. AB AiÀÄ£ÀÄß ‘x’ ©AzÀÄ«£À°è ¸Àà²ð¸ÀÄªÀAvÉAiÀÄÆ ªÀÄvÀÄÛ (ªÉÆzÀ®Ä J¼ÉzÀ) ªÀÈvÀÛªÀ£ÀÄß ¨ÁºÀåªÁV ¸Àà²ð¸ÀÄªÀAvÉ E£ÉÆßAzÀÄ ªÀÈvÀÛªÀ£ÀÄß J¼É¬Äj.

Draw a circle of radius 2 cms. Produce OB, a radius of this circle to ‘x’ so that BX=2 cms. Construct a circle to touch AB at ‘x’ and to touch the circle (drawn earlier) externally. 7 A,S 2+1 D

M036 ∆ABC zÀÀ°è BDAiÀÄÄ ‘B’ ªÀÄÆ®PÀ J¼ÉzÀ JvÀÛgÀªÁVzÉ ªÀÄvÀÄÛ AD : CD = 1:2. DVzÉ. AC2=3 (BC2-AB2)

BD is the altitude through ‘B’ in the ∆ABC and AD : CD = 1:2. Prove that AC2=3 (BC2-AB2) 8 U,S 1+2 A

M037 F avÀæzÀ°è AB \\ CD , AB = 9 ¸ÉA.«Ä, DE = 4¸ÉA,«Ä, CE = 5 ¸ÉA.«Ä ªÀÄvÀÄÛ CD = 6 ¸ÉA.«Ä DzÀgÉ BE AiÀÄ C¼ÀvÉAiÀÄ£ÀÄß PÀAqÀÄ»r¬Äj. 9

A B 4 5 D C 6 In the adjoining figure AB \\ CD, AB = 9 cm, DE = 4cm, CE = 5 cm and CD = 6 cm. Find BE

9 A B 4 5 D C 6 8 U,A 1+2 A

M038 JgÀqÀÄ ¸ÀªÀÄgÀÆ¥À wæ sÀÄdzÀ C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼ÀÄÀ 9 ÉA.«Ä ªÀÄvÀÄÛ 6 ÉA.«Ä DVzÀÝgÉ. F ¨ÁºÀÄUÀ½UÉ J¼ÉzÀ ®A§UÀ¼À C£ÀÄ¥ÁvÀªÀ£ÀÄß PÀAqÀÄ »r¬Äj.

Corresponding sides of two similar triangles are 9 cm and 6 cm. Find the ratio of their altitudes drawn to those two sides. 8 U,S 1+2 A

E

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Level

M039 44«ÄÃlgï JvÀÛgÀ«gÀÄªÀ PÀlÖqÀªÀÅ 66 «ÄÃlgï GzÀÝzÀ £ÉgÀ¼À£ÀÄß £É®zÀ ªÉÄÃ¯É ©Ã¼ÀÄªÀAvÉ ªÀiÁrzÀgÉ CzÉÃ ¸ÀªÀÄAiÀÄzÀ°è 6 «ÄÃlgï JvÀÛgÀzÀ ªÀÄgÀªÀÅ GAlÄªÀiÁqÀÄªÀ £ÉgÀ½£À GzÀÝªÉÃµÀÄÖ?

The length of the shadow cast by a building of height 44 mts is 66 mts on the ground. At the same time length of the shadow cast by a tree is 6 mts. What is the vertical height of the tree? 8 U,S 1+2 A

M040 MAzÀÄ ªÀÄgÀzÀ DnPÉAiÀÄ DPÁgÀªÀÅ, CzsÀðUÉÆ¼ÀzÀ ªÉÄÃ¯É, MAzÀÄ ±ÀAPÀÄªÀ£ÀÄß ¤°è¹zÀAwzÉ. CzsÀðUÉÆÃ¼À ªÀÄvÀÄÛ ±ÀAPÀÄ«£À wædåUÀ¼ÀÄ vÀ Á 4.2 ÉA.«Ä ªÀÄvÀÄÛ MlÄÖ DnPÉAiÀÄ JvÀÛgÀªÀÅ 4.2 ¸ÉA,«Ä DVzÉ. DnPÉUÉ ¨ÉÃPÁUÀÄªÀ ªÀÄgÀzÀ UávÀæªÀ£ÀÄß ¯ÉQÌ¹.

A solid wooden toy is in the form of a cone mounted on a hemisphere. The radii of the hemisphere and the base of the cone are 4.2 cms each and the total height of the toy is 10.2 cms. Calculate volume of wood used in the toy. 9 K,S 1+2 A

M041 PÀæªÀÄªÁV 3 ,4 ªÀÄvÀÄÛ 3 ªÀUð«gÀÄªÀ A, B ªÀÄvÀÄÛ C ¸ÀA¥ÁvÀ ©ªÀÄzÀÄUÀ½gÀÄªÀ eÁ¯ÁPÀÈwAiÀÄ£ÀÄß gÀa¹.

Construct a network of 3 nodes A, B,C which are of the order 3 ,4 and 3 respectively 10 K,S 1+2 A

M042 MAzÀÄ PÀAvÀÄ ªÁå¥ÁgÀzÀ AiÉÆÃd£ÉAiÀÄ°è PÁgÀ£ÀÄß PÉÆ¼Àî§ºÀÄzÁVzÉ. ¥ÁægÀA¨sÀzÀ°è 5gÀÆ dªÉÄ ªÀiÁr, D wAUÀ¼À PÉÆ£ÉAiÀÄ°è 10gÀÆ £ÀÄß C£AvÀgÀzÀ ¥Àæw wAUÀ¼À PÉÆ£ÉAiÀÄ°è »A¢£À wAUÀ¼À PÀAw£À ªÉÆ§®V£À JgÀqgÀµÀÖgÀAvÉ ºÀt PÀlÖ¨ÉÃPÀÄ. ºÁUÉ M§â£ÀÄ 17£É PÀAw£À°è gÀÆ. 3,27,680 PÀnÖzÀgÉ, CªÀ£ÀÄ PÀnÖzÀ MlÄÖ ªÉÆvÀÛªÀ£ÀÄß AiÀiÁªÀÅzÁzÀgÀÆ ±ÉæÃrüAiÀÄ vÀvÀéªÀ£ÀÄß G¥ÀAiÉÆÃV¹ PÀAqÀÄ»r¬Äj.

In an instalment purchase scheme for cars, a buyer has to pay Rs.5 initially and Rs.10 at the end of that month. Further he has to pay double the previous amount at the end of each month. If the 17th instalment paid is Rs. 3,27,680. Find total amount paid using principles of progressions. 1 A,S 2+2 A

M043 MAzÀÄ ªÁºÀ£ÀzÀ ¸ÁªÀiÁ£ÀåªÉÃUÀªÀ£ÀÄß WÀAmÉUÉ 5 Q.«Ä £ÀµÀÄÖ vÀVÎ¹zÀgÉ, ªÁºÀ£ÀªÀÅ 300 Q.«Ä zÀÆgÀªÀ£ÀÄß PÀæ«Ä¸À®Ä 2WÀAmÉ ºÉZÀÄÑ vÉUÉzÀÄPÉÆ¼ÀÄîvÀÛzÉÉ. ºÁUÁzÀgÉ CzÀgÀ ¸ÁªÀiÁ£ÀåªÉÃUÀªÀ£ÀÄß PÀAqÀÄ»r¬Äj?

If the usual speed of a vehicle is reduced by 5 km per hour, it takes 2 hrs more to cover a distance of 300 kms. Find the usual speed. 5 K,S 2+2 E

M044 2.5 ¸ÉA.«Ä wædåªÀÅ¼ÀîÀ ªÀÈvÀÛPÉÌ ‘P’ ©AzÀÄ«£À°è MAzÀÄ QPR ¸Àà±ÀðPÀªÀ£ÀÄß gÀa¹j. ªÀÈvÀÛzÀ ºÉÆgÀUÉ ¸Àà±ÀðPÀzÀ ªÉÄÃ°®èzÀ MAzÀÄ ©AzÀÄ ‘S’ ªÀ£ÀÄß UÀÄgÀÄw¹. ¥ÁæAiÉÆÃVPÀªÀzsÁ£À¢AzÀ JgÀqÀ£ÉÃ ¸Àà±ÀðPÀ SPT ªÀ£ÀÄß gÀa¸À®Ä ¸ÁzsÀå«®è JAzÀÄ vÉÆÃj¹.

Draw a tangent QPR to a circle of radius 2.5 cms at any point ‘P’ on it. Mark a point ‘S’ outside the circle and not on QPR. By practical method show that a second tangent SPT cannot be drawn. 7 A,S 2+2 A

M045 JgÀqÀÄ wæ sÀÄdUÀ¼ÀÄ ¸ÀªÀÄ PÉÆÃ£ÀUÀ¼ÁVzÀÝgÉ, CªÀÅUÀ¼À C£ÀÄgÀÆ¥À ¨ÁºÀÄUÀ¼ÀÄ ¸ÀªÀiÁ£ÀÄ¥ÁvÀzÀ°ègÀÄvÀÛªÉ, ¸Á¢ü¹.

Prove that if two triangles are equiangular, then their corresponding sides are proportional. 8 K,S 2+2 E

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Kannada Hindi

Sri.B.S.Gundu Rao, Deputy Director , Gandhi Centre for Peace and Human Values Bangalore

Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum Dr. Ispak Ali, Lalbahudar Sastry B.Ed College, Bangalore

Sri.C.S. Banashankariah, Bangalore Sri. Abdul Nazir, Q.Islam HS, Bangalore

Sri. P.Dharukaradhya, Basaveshwara Girls High School, B’lore Sri. G.H. Balakrishna, Bangalore

Sri.N.Gopal Krishna Udupa, Bangalore Smt. Shyalaja H.Naidu, DPH HS, Bangalore

Smt. Prema H.Tahsildar, Bharati Vidyalaya, Khasbag, Belgaum Smt. Urmilla Nahar, DPH HS, Bangalore

Smt.Bhuvaneshwari.G.S, Women’s Peace league, Bangalore Sri. Anand.S. Kalasad, KC PU College, Hirebagewadi, Belgaum

Smt. Bhagirathi Bhat, GHS, Ketamaranahalli, Bangalore Sri. Ashok.H.Balunnavar, MM Comp. PU College, Belgaum

Smt. Vasundhara M.G, Bharatamata Vidyamandir, Bangalore Smt. Geetanjali.P.Yogi, Benson’s HS, Belgaum

Sri. V. Krishnaiah, Sir M.V. Comp. PU College, Bangalore Dr.Bharati T.Savadattu, Govt. Saraswathi PU College, Belgaum

Smt. S. Padmavathi, Vidya Vardhaka Sangha, Bangalore Dr. K.L.Sattigeri, Principal, Dr. B.D. Jatti COE, Belgaum

Sri.Nagaraj.S, Vivekananda Vidya Kendra, Bangalore Urdu

Smt. Kannika, Sri Aravind Vidya Mandira, Bangalore Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum

Smt. Srilata G.S, MES Kishore Kendra, Bangalore Smt. Shaheda Perveen, BRP, Shankarapura, Bangalore

English Sri. Bahadur Khan, MO Girls HS, Bangalore

Prof. G.S. Mudambadithaya, Bangalore Sri.S.G. Deshnoor, Al-Ameen HS, Belgaum

Sri.A.P. Gundappa, Attibele Sri. F.A. Yallur, Islamai Girls High School, Belgaum

Smt. Umadevi, R.V.Girls High School, Bangalore Sri.D.M. Momin, Bashiban High School, Belgaum

Smt. Maya Ramchand, Bangalore Marati

Smt. Shobha Kulkarni, Govt. Sardar HS, Belgaum Sri. M.L. Dakhani, Advisor, Dr. B.D. Jatti COE, Belgaum

Sri.Sathya Prakash, Vidya Vardhaka Sangha HS, Bangalore Smt.Shaila.V.M, Mahila Vidyalaya HS, Belgaum

Smt. Asha, Saraswathi Vidya Mandir, Bangalore Smt. Sunitha.D. Mathad, Ushatai Gogate Girls HS, Belgaum

Smt. Prameetha Adoni, HM, GHS, KR Puram, Bangalore Sri. P.T. Malege, MM Comp. PU College, Belgaum

Sri.G.N. Deshpande, HM, BN Darbar GHS, Bijapur Sri. C.Y. Patil, Talakwadi HS, Belgaum

Sri. Shankaranarayana Rao.P , SS High School, Kadandale, DK Sri. A.L. Patil, MM Central HS, Belgaum

Smt. Lata Rao, HM, SJR High School, Bangalore Smt. Sheela Deshpande, LBS B.Ed College, Bangalore

Sanskrit Science

Dr. Satish Hegde, R.V. Girls High School, Bangalore Dr. Sameera Simha, Vijaya Teachers College, Bangalore

Sri. Shridhar Hegde, National High School, Bangalore Dr. S. Srikanta Swamy, R.V. Teachers College, Bangalore

Sri. Narayan Ananth Bhat,Govt PU College, Chamarajpet, B’lore Sri.P.G.Dwarakanath, Vidya Vardhaka Sangha, Bangalore

Sri.Venkataramana D.Bhat, Govt Jr. College, Vartur, B’lore Dr.R.Mythili, Associate Director, RVEC, Bangalore

Sri.Narasimha Bhagavat, Janaseva Vidya Kendra, Chennenahalli Smt. Shantha Kumari.B.S., Bangalore

Smt. Shylaja.V, Chamarajpet Jr. College, Bangalore Smt. Vasanthi Rao, Bangalore

Sri. Krishna V. Bhat, Vasavi Vidyaniketan, Bangalore Smt. Rekha Hegde, Vani High School, Bangalore Sri. Mahesh Bhat, PTA High School, Bangalore Smt. K.S. Shyamala, HM, Vasavi High School, Bangalore Sri. Balasubramanian, Methodist HS, Kolar Smt. R. Geetha, Vasavi High School, Bangalore Smt. Geeta B.S, Seshadripuram GHS, Bangalore Smt. S.K. Prabha, Retd. Lecturer, DIET, Bangalore Telugu Smt. Bhagyalakshmi, Stella Mari’s School, Bangalore Dr. T.K. Jayalakshmi, Director, RVEC, Bangalore Smt. V. Padma, Vidya Vardhaka Sangha HS, Bangalore Sri. Nagesam.C, RBANM High School, Bangalore Social Studies

Sri. G. Venkata Rama Reddy, Telugu Pandit, Bangalore Prof. G.P. Basavaraj, Retd Director, NCERT Sri. P.Hema Chendra Babu, Telugu Pandit, Bangalore Sri. P.A. Kumar, HM, Vijaya High School, Bangalore Tamil Prof. B.R. Gopal, MES Teachers College, Bangalore Prof. Susheela Sheshadri, Principal, Amrita Shikshana M.Vidyala,Mysore Smt. Lorna Pinto, SAM High School, Bangalore Sri. Pulavar V. Vishwanathan, Bangalore Smt. Radhika.S, Hymamshu Jyothi Kala Kendra, Bangalore Sri.S.Ramalingam, Seva Ashram High School, Bangalore Smt. T.R. Sandhyavalli, Basaveshwara Jr. College, Bangalore Sri.G. Sampath, Bangalore Smt. R. Vijayavalli, Nirmala Rani GHS, Bangalore Mathematics Smt. Shamala Prasad, MES Kishore Kendra, Bangalore Dr. D.S. Shivananda, Bangalore Smt. Sukanya.N.R, Sardar Patil HS, Bangalore Sri. Kailash Nekraj, HM, Jnanamitra HS, Bangalore Smt. Meera, Vidya Vardhaka Sangha HS, Bangalore Sri.N.C. Satyaji Rao, Bangalore Smt. N.S. Vyjayanthi, Vidya Bharathi Eng. School, Bangalore Smt. K.S. Susheela, Bangalore Smt. Lakshamma, Bangalore Smt. Subhadra.M.S, Bangalore Smt. C. Nirmala, HM, MABL HS, Doddaballapura Dr.T.K. Jayalakshmi, Director, RVEC, Bangalore Dr. R. Mythili, Associate Director, Bangalore

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